Data processing apparatus and method

ABSTRACT

A data processing apparatus includes a group-wise interleaving unit that performs group-wise interleaving; and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction. A type of the block interleaving includes a type A and a type B. A MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority of U.S. Provisional Application Ser. No. 62/102,941, filed Jan. 13, 2015, and U.S. Provisional Application Ser. No. 62/105,494, filed Jan. 20, 2015, the entire contents of which are incorporated herein by reference.

BACKGROUND

The present technology relates to a data processing apparatus and a data processing method, and more specifically, it relates to a data processing apparatus and a data processing method capable of allowing a plurality of block interleaving methods to efficiently coexist in data transmission using, for example, an LDPC code.

Some information described in the present specification and drawings is offered from Samsung Electronics Co., Ltd. (hereinafter, referred to as Samsung), LGE Inc., the NERC, and CRC/ETRI (specified in the drawing).

A low density parity check (LDPC) code has high error correcting capability, and has been widely used in transmission schemes of digital broadcasting such as digital video broadcasting (DVB)-S.2, DVB-T.2 or DVB-C.2 in Europe, and advanced television systems committee (ATSC) 3.0 in the United States (for example, see DVB-S2X: ETSI EN 302 307-2 V1.1.1 (2014-10)) in recent years.

According to recent research, similarly to a turbo code, when the LDPC code is used, it has been found that it is possible to obtain performance approximate to the Shannon limit having long code length. Since the LDPC code has the feature that a minimum distance is proportional to a code length, the LDPC code features good block error probability characteristics, and has a merit that a so-called error floor phenomenon which is observed in decoding characteristics on the turbo code does not occur.

SUMMARY

For example, in the data transmission using the LDPC code, the LDPC code is changed (is symbolized) to a symbol of quadrature modulation (digital modulation) such as quadrature phase shift keying (QPSK), and the symbol is mapped to a signal point of quadrature modulation and is transmitted. The data transmission using the LDPC code described above has been widely used all over the world.

However, when bit interleaving is performed on the LDPC code, a plurality of block interleaving methods may be adopted, and the plurality of block interleaving methods have to efficiently coexist.

The present technology has been made in view of such circumstances, and it is possible to allow a plurality of block interleaving methods to efficiently coexist in data transmission using an LDPC code.

According to an embodiment of the present technology, there is provided a first data processing apparatus/method. The first data processing apparatus/method is a data processing apparatus/method including a group-wise interleaving unit/group-wise interleaving that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits; and a block interleaving unit/block interleaving that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme. A type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed. A MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed. When the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit/group-wise interleaving performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit/group-wise interleaving performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.

In the first data processing apparatus/method, group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits is performed, and block interleaving is performed in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme. A type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed. A MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed. When the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, in the group-wise interleaving, the group-wise interleaving is performed on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, in the group-wise interleaving, the group-wise interleaving is performed on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.

According to another embodiment of the present technology, there is provided a second data processing apparatus/method. The second data processing apparatus/method is a data processing apparatus/method including a block deinterleaving unit/block deinterleaving that performs block deinterleaving which returns m bits of a symbol obtained from data transmitted from a transmission apparatus to an LDPC code obtained by performing group-wise interleaving; and a group-wise deinterleaving unit/group-wise deinterleaving that performs group-wise deinterleaving which returns the arrangement of the LDPC code obtained by performing the group-wise interleaving on the original arrangement. The transmission apparatus includes a group-wise interleaving unit that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits, and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme. A type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed. A MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed. When the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.

In the second data processing apparatus/method, block deinterleaving which returns m bits of a symbol obtained from data transmitted from a transmission apparatus to an LDPC code obtained by performing group-wise interleaving is performed, and group-wise deinterleaving which returns the arrangement of the LDPC code obtained by performing the group-wise interleaving on the original arrangement is performed. The transmission apparatus includes a group-wise interleaving unit that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits, and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme. A type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed. A MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed. When the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.

The data processing apparatuses may be one independent apparatus, or may be internal blocks constituting one apparatus.

According to the present technology, it is possible to allow a plurality of block interleaving methods to efficiently coexist in data transmission using an LDPC code.

The effects described herein are not necessarily limited, and may be any one of the effects described in the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram for describing a parity check matrix H of an LDPC code;

FIG. 2 is a flowchart for describing a decoding procedure of the LDPC code;

FIG. 3 is a diagram showing an example of the parity check matrix of the LDPC code;

FIG. 4 is a diagram showing an example of a Tanner graph of the parity check matrix;

FIG. 5 is a diagram showing an example of a variable node;

FIG. 6 is a diagram showing an example of a check node;

FIG. 7 is a diagram showing a configuration example of an embodiment of a transmission system to which the present technology is applied;

FIG. 8 is a block diagram showing a configuration example of a transmission apparatus;

FIG. 9 is a block diagram showing a configuration example of a bit interleaver;

FIG. 10 is a diagram showing an example of the parity check matrix;

FIG. 11 is a diagram showing an example of a parity matrix;

FIG. 12 is a diagram for describing a parity check matrix of an LDPC code defined by the standard of DVB-T.2;

FIG. 13 is a diagram for describing the parity check matrix of the LDPC code defined by the standard of DVB-T.2;

FIG. 14 is a diagram showing an example of a Tanner graph for the decoding of the LDPC code;

FIGS. 15A and 15B are diagrams showing examples of a parity matrix having a dual diagonal structure and a Tanner graph corresponding to the parity matrix;

FIG. 16 is a diagram showing an example of the parity matrix of the parity check matrix corresponding to the LDPC code on which parity interleaving has been performed;

FIG. 17 is a flowchart for describing an example of a process performed in the bit interleaver and a mapper;

FIG. 18 is a block diagram showing a configuration example of an LDPC encoder;

FIG. 19 is a flowchart for describing an example of the process of the LDPC encoder;

FIG. 20 is a diagram showing an example of a parity check matrix initial value table in which a code rate is 1/4 and a code length is 16,200;

FIG. 21 is a diagram for describing a method of obtaining the parity check matrix H from the parity check matrix initial value table;

FIG. 22 is a diagram showing a structure of the parity check matrix;

FIG. 23 is a diagram showing an example of the parity check matrix initial value table;

FIG. 24 is a diagram for describing an A matrix generated from the parity check matrix initial value table;

FIG. 25 is a diagram for describing parity interleaving on a B matrix;

FIG. 26 is a diagram for describing a C matrix generated from the parity check matrix initial value table;

FIG. 27 is a diagram for describing parity interleaving on a D matrix;

FIG. 28 is a diagram showing a parity check matrix obtained by performing column permutation as parity interleaving that returns the parity interleaving to an original state on the parity check matrix;

FIG. 29 is a diagram showing a transformation check matrix obtained by performing row permutation on the parity check matrix;

FIG. 30 is a diagram showing an example of the parity check matrix initial value table;

FIG. 31 is a diagram showing an example of the parity check matrix initial value table;

FIG. 32 is a diagram showing an example of the parity check matrix initial value table;

FIG. 33 is a diagram showing an example of the parity check matrix initial value table;

FIG. 34 is a diagram showing an example of the parity check matrix initial value table;

FIG. 35 is a diagram showing an example of the parity check matrix initial value table;

FIG. 36 is a diagram showing an example of the parity check matrix initial value table;

FIG. 37 is a diagram showing an example of the parity check matrix initial value table;

FIG. 38 is a diagram showing an example of the parity check matrix initial value table;

FIG. 39 is a diagram showing an example of the parity check matrix initial value table;

FIG. 40 is a diagram showing an example of the parity check matrix initial value table;

FIG. 41 is a diagram showing an example of the parity check matrix initial value table;

FIG. 42 is a diagram showing an example of the parity check matrix initial value table;

FIG. 43 is a diagram showing an example of the parity check matrix initial value table;

FIG. 44 is a diagram showing an example of the parity check matrix initial value table;

FIG. 45 is a diagram showing an example of the parity check matrix initial value table;

FIG. 46 is a diagram showing an example of the parity check matrix initial value table;

FIG. 47 is a diagram showing an example of the parity check matrix initial value table;

FIG. 48 is a diagram showing an example of the parity check matrix initial value table;

FIG. 49 is a diagram showing an example of the parity check matrix initial value table;

FIG. 50 is a diagram showing an example of the parity check matrix initial value table;

FIG. 51 is a diagram showing an example of the parity check matrix initial value table;

FIG. 52 is a diagram showing an example of the parity check matrix initial value table;

FIG. 53 is a diagram showing an example of the parity check matrix initial value table;

FIG. 54 is a diagram showing an example of the parity check matrix initial value table;

FIG. 55 is a diagram showing an example of the parity check matrix initial value table;

FIG. 56 is a diagram showing an example of the parity check matrix initial value table;

FIG. 57 is a diagram showing an example of the parity check matrix initial value table;

FIG. 58 is a diagram showing an example of the parity check matrix initial value table;

FIG. 59 is a diagram showing an example of the parity check matrix initial value table;

FIG. 60 is a diagram showing an example of the parity check matrix initial value table;

FIG. 61 is a diagram showing an example of the parity check matrix initial value table;

FIG. 62 is a diagram showing an example of the parity check matrix initial value table;

FIG. 63 is a diagram showing an example of the parity check matrix initial value table;

FIG. 64 is a diagram showing an example of the parity check matrix initial value table;

FIG. 65 is a diagram showing an example of the parity check matrix initial value table;

FIG. 66 is a diagram showing an example of the parity check matrix initial value table;

FIG. 67 is a diagram showing an example of the parity check matrix initial value table;

FIG. 68 is a diagram showing an example of the parity check matrix initial value table;

FIG. 69 is a diagram showing an example of the parity check matrix initial value table;

FIG. 70 is a diagram showing an example of the parity check matrix initial value table;

FIG. 71 is a diagram showing an example of the parity check matrix initial value table;

FIG. 72 is a diagram showing an example of the parity check matrix initial value table;

FIG. 73 shows an example of a Tanner graph of a degree sequence ensemble in which column weights are 3 and row weights are 6;

FIG. 74 shows an example of a Tanner graph of a multi-edge type ensemble;

FIG. 75 is a diagram for describing the parity check matrix;

FIG. 76 is a diagram for describing the parity check matrix;

FIG. 77 is a diagram for describing the parity check matrix;

FIG. 78 is a diagram for describing the parity check matrix;

FIG. 79 is a diagram for describing the parity check matrix;

FIG. 80 is a diagram for describing the parity check matrix;

FIG. 81 is a diagram for describing the parity check matrix;

FIG. 82 is a diagram for describing the parity check matrix;

FIG. 83 is a diagram showing an example of a constellation when a modulation scheme is 16-QAM;

FIG. 84 is a diagram showing an example of a constellation when a modulation scheme is 64-QAM;

FIG. 85 is a diagram showing an example of a constellation when a modulation scheme is 256-QAM;

FIG. 86 is a diagram showing an example of a constellation when a modulation scheme is 1024-QAM;

FIG. 87 is a diagram showing an example of a constellation when a modulation scheme is 4096-QAM;

FIG. 88 is a diagram showing an example of a constellation when a modulation scheme is 4096-QAM;

FIG. 89 is a diagram showing an example of a coordinate of a signal point of UC when a modulation scheme is QPSK;

FIG. 90 is a diagram showing an example of a coordinate of a signal point of 2D NUC when a modulation scheme is 16-QAM;

FIG. 91 is a diagram showing an example of a coordinate of a signal point of 2D NUC when a modulation scheme is 64-QAM;

FIG. 92 is a diagram showing an example of a coordinate of a signal point of 2D NUC when a modulation scheme is 256-QAM;

FIG. 93 is a diagram showing an example of a coordinate of a signal point of 2D NUC when a modulation scheme is 256-QAM;

FIG. 94 is a diagram showing an example of a coordinate of a signal point of 1D NUC when a modulation scheme is 1024-QAM;

FIGS. 95A and 95B are diagrams showing the relationship between a symbol of 1024-QAM and a real part and an imaginary part of a complex number as a coordinate of a signal point of the 1D NUC corresponding to the symbol;

FIG. 96 is a diagram showing an example of the coordinate of the signal point of the 1D NUC when the modulation scheme is 4096-QAM;

FIGS. 97A and 97B are diagrams showing the relationship between the symbol of 4096-QAM and the real part and the imaginary part of the complex number as the coordinate of the signal point of the 1D NUC corresponding to the symbol;

FIG. 98 is a diagram showing another example of a constellation when a modulation scheme is 16-QAM;

FIG. 99 is a diagram showing another example of a constellation when a modulation scheme is 64-QAM;

FIG. 100 is a diagram showing another example of a constellation when a modulation scheme is 256-QAM;

FIG. 101 is a diagram showing another example of a coordinate of a signal point of 2D NUC when a modulation scheme is 16-QAM;

FIG. 102 is a diagram showing another example of a coordinate of a signal point of 2D NUC when a modulation scheme is 64-QAM;

FIG. 103 is a diagram showing another example of a coordinate of a signal point of 2D NUC when a modulation scheme is 256-QAM;

FIG. 104 is a diagram showing another example of a coordinate of a signal point of 2D NUC when a modulation scheme is 256-QAM;

FIG. 105 is a block diagram showing a configuration example of a block interleaver;

FIG. 106 is a diagram showing the number of columns of parts for combinations of code lengths and modulation schemes and part column lengths;

FIGS. 107A and 107B are diagrams for describing block interleaving performed in the block interleaver;

FIG. 108 is a diagram for describing group-wise interleaving performed in a group-wise interleaver;

FIG. 109 is a diagram showing a first example of a GW pattern for an LDPC code having a code length of 64 k bits;

FIG. 110 is a diagram showing a second example of the GW pattern for the LDPC code having a code length of 64 k bits;

FIG. 111 is a diagram showing a third example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 112 is a diagram showing a fourth example of the GW pattern for the LDPC code having the code length of 64 k bits.

FIG. 113 is a diagram showing a fifth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 114 is a diagram showing a sixth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 115 is a diagram showing a seventh example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 116 is a diagram showing an eighth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 117 is a diagram showing a ninth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 118 is a diagram showing a tenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 119 is a diagram showing an eleventh example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 120 is a diagram showing a twelfth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 121 is a diagram showing a thirteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 122 is a diagram showing a fourteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 123 is a diagram showing a fifteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 124 is a diagram showing a sixteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 125 is a diagram showing a seventeenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 126 is a diagram showing an eighteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 127 is a diagram showing a nineteenth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 128 is a diagram showing a twentieth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 129 is a diagram showing a twenty-first example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 130 is a diagram showing a twenty-second example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 131 is a diagram showing a twenty-third example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 132 is a diagram showing a twenty-fourth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 133 is a diagram showing a twenty-fifth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 134 is a diagram showing a twenty-sixth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 135 is a diagram showing a twenty-seventh example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 136 is a diagram showing a twenty-eighth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 137 is a diagram showing a twenty-ninth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 138 is a diagram showing a thirtieth example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 139 is a diagram showing a thirty-first example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 140 is a diagram showing a thirty-second example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 141 is a diagram showing a thirty-third example of the GW pattern for the LDPC code having the code length of 64 k bits;

FIG. 142 is a diagram showing a first example of a GW pattern for an LDPC code having a code length of 16 k bits;

FIG. 143 is a diagram showing a second example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 144 is a diagram showing a third example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 145 is a diagram showing a fourth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 146 is a diagram showing a fifth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 147 is a diagram showing a sixth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 148 is a diagram showing a seventh example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 149 is a diagram showing an eighth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 150 is a diagram showing a ninth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 151 is a diagram showing a tenth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 152 is a diagram showing an eleventh example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 153 is a diagram showing a twelfth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 154 is a diagram showing a thirteenth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 155 is a diagram showing a fourteenth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 156 is a diagram showing a fifteenth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 157 is a diagram showing a sixteenth example of the GW pattern for the LDPC code having the code length of 16 k bits;

FIG. 158 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 159 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 160 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 161 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 162 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 163 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 164 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 165 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 166 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 167 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 168 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 169 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 170 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 171 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 172 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 173 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 174 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 175 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 176 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 177 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 178 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 179 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 180 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 181 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 182 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 183 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 184 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 185 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 186 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 187 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 188 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 189 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 190 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 191 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 192 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 193 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 194 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 195 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 196 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 197 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 198 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 199 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 200 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 201 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 202 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 203 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 204 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 205 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 206 is a diagram showing a simulation result of a simulation that measures an error rate;

FIG. 207 is a block diagram showing a configuration example of the reception apparatus;

FIG. 208 is a block diagram showing a configuration example of a bit deinterleaver;

FIG. 209 is a flowchart for describing an example of the process performed by a demapper, the bit deinterleaver and an LDPC decoder;

FIG. 210 is a diagram showing an example of a parity check matrix of the LDPC code;

FIG. 211 is a diagram showing an example of a matrix (transformation check matrix) obtained by performing row permutation and column permutation on the parity check matrix;

FIG. 212 is a diagram showing an example of the transformation check matrix divided into a unit of a 5×5 matrix;

FIG. 213 is a block diagram showing a configuration example of a decoding device that performs node calculation P times all at once;

FIG. 214 is a block diagram showing a configuration example of the LDPC decoder;

FIG. 215 is a block diagram showing a configuration example of a block deinterleaver;

FIG. 216 is a block diagram showing another configuration example of the bit deinterleaver;

FIG. 217 is a block diagram showing a configuration example of the bit interleaver;

FIG. 218 is a block diagram showing a configuration example of a block interleaver corresponding to block interleaving of a type A;

FIG. 219 is a diagram showing the number of columns of parts for combinations of code lengths and modulation schemes and part column lengths;

FIGS. 220A and 220B are diagrams for describing block interleaving performed in the block interleaver corresponding to the block interleaving of the type A;

FIG. 221 is a diagram for describing group-wise interleaving performed in a group-wise interleaver;

FIG. 222 is a diagram for describing a specific example (case 1) of the block interleaving of the type A;

FIG. 223 is a diagram for describing a specific example (case 2) of the block interleaving of the type A;

FIG. 224 is a block diagram showing a configuration example of the block interleaver corresponding to block interleaving of a type B;

FIGS. 225A and 225B are diagrams for describing block interleaving performed in the block interleaver corresponding to the block interleaving of the type B;

FIG. 226 is a diagram for describing a specific example (case 1) of the block interleaving of the type B;

FIG. 227 is a diagram for describing a specific example (case 2) of the block interleaving of the type B;

FIG. 228 a diagram for describing a specific conversion example (case 1) of the GW pattern performed in the group-wise interleaver;

FIG. 229 is a diagram for describing a specific conversion example (case 2) of the GW pattern performed in the group-wise interleaver;

FIG. 230 shows an example of the GW pattern set to a MODCOD which is the combination of the LDPC code of 64 k bits and the modulation scheme;

FIG. 231 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 2/15;

FIG. 232 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 3/15;

FIG. 233 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 4/15;

FIG. 234 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 5/15;

FIG. 235 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 6/15;

FIG. 236 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 7/15;

FIG. 237 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 8/15;

FIG. 238 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 9/15;

FIG. 239 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 10/15;

FIG. 240 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 11/15;

FIG. 241 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 12/15;

FIG. 242 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is QPSK and the code rate is 13/15;

FIG. 243 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 2/15;

FIG. 244 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 3/15;

FIG. 245 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 4/15;

FIG. 246 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 5/15;

FIG. 247 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 6/15;

FIG. 248 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 7/15;

FIG. 249 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 8/15;

FIG. 250 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 9/15;

FIG. 251 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 10/15;

FIG. 252 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 11/15;

FIG. 253 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 12/15;

FIG. 254 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 16-QAM and the code rate is 13/15;

FIG. 255 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 2/15;

FIG. 256 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 3/15;

FIG. 257 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 4/15;

FIG. 258 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 5/15;

FIG. 259 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 6/15;

FIG. 260 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 7/15;

FIG. 261 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 8/15;

FIG. 262 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 9/15;

FIG. 263 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 10/15;

FIG. 264 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 11/15;

FIG. 265 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 12/15;

FIG. 266 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 64-QAM and the code rate is 13/15;

FIG. 267 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 2/15;

FIG. 268 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 3/15;

FIG. 269 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 4/15;

FIG. 270 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 5/15;

FIG. 271 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 6/15;

FIG. 272 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 7/15;

FIG. 273 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 8/15;

FIG. 274 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 9/15;

FIG. 275 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 10/15;

FIG. 276 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 11/15;

FIG. 277 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 12/15;

FIG. 278 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 256-QAM and the code rate is 13/15;

FIG. 279 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 2/15;

FIG. 280 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 3/15;

FIG. 281 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 4/15;

FIG. 282 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 5/15;

FIG. 283 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 6/15;

FIG. 284 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 7/15;

FIG. 285 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 8/15;

FIG. 286 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 9/15;

FIG. 287 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 10/15;

FIG. 288 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 11/15;

FIG. 289 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 12/15;

FIG. 290 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM and the code rate is 13/15;

FIG. 291 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 2/15;

FIG. 292 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 3/15;

FIG. 293 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 4/15;

FIG. 294 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 5/15;

FIG. 295 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 6/15;

FIG. 296 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 7/15;

FIG. 297 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 8/15;

FIG. 298 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 9/15;

FIG. 299 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 10/15;

FIG. 300 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 11/15;

FIG. 301 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 12/15;

FIG. 302 is a diagram showing an example of the GW pattern for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM and the code rate is 13/15;

FIG. 303 shows an example of the GW pattern set to a MODCOD which is the combination of the modulation scheme and the LDPC code of 16 k bits;

FIG. 304 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 2/15;

FIG. 305 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 3/15;

FIG. 306 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 4/15;

FIG. 307 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 5/15;

FIG. 308 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 6/15;

FIG. 309 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 7/15;

FIG. 310 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 8/15;

FIG. 311 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 9/15;

FIG. 312 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 10/15;

FIG. 313 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 11/15;

FIG. 314 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 12/15;

FIG. 315 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is QPSK and the code rate is 13/15;

FIG. 316 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 2/15;

FIG. 317 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 3/15;

FIG. 318 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 4/15;

FIG. 319 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 5/15;

FIG. 320 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 6/15;

FIG. 321 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 7/15;

FIG. 322 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 8/15;

FIG. 323 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 9/15;

FIG. 324 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 10/15;

FIG. 325 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 11/15;

FIG. 326 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 12/15;

FIG. 327 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 16-QAM and the code rate is 13/15;

FIG. 328 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 2/15;

FIG. 329 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 3/15;

FIG. 330 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 4/15;

FIG. 331 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 5/15;

FIG. 332 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 6/15;

FIG. 333 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 7/15;

FIG. 334 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 8/15;

FIG. 335 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 9/15;

FIG. 336 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 10/15;

FIG. 337 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 11/15;

FIG. 338 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 12/15;

FIG. 339 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 64-QAM and the code rate is 13/15;

FIG. 340 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 2/15;

FIG. 341 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 3/15;

FIG. 342 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 4/15;

FIG. 343 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 5/15;

FIG. 344 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 6/15;

FIG. 345 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 7/15;

FIG. 346 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 8/15;

FIG. 347 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 9/15;

FIG. 348 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 10/15;

FIG. 349 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 11/15;

FIG. 350 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 12/15;

FIG. 351 is a diagram showing an example of the GW pattern for the LDPC code of 16 k bits when the modulation scheme is 256-QAM and the code rate is 13/15;

FIG. 352 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is QPSK;

FIG. 353 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is 16-QAM;

FIG. 354 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is 64-QAM;

FIG. 355 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is 256-QAM;

FIG. 356 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is 1024-QAM;

FIG. 357 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 64 k bits when the modulation scheme is 4096-QAM;

FIG. 358 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 16 k bits when the modulation scheme is QPSK;

FIG. 359 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 16 k bits when the modulation scheme is 16-QAM;

FIG. 360 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 16 k bits when the modulation scheme is 64-QAM;

FIG. 361 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code of 16 k bits when the modulation scheme is 256-QAM;

FIG. 362 is a block diagram showing a configuration example of the bit deinterleaver;

FIG. 363 is a block diagram showing a configuration example of a block deinterleaver corresponding to block deinterleaving of a type A;

FIG. 364 is a block diagram showing a configuration example of the block deinterleaver corresponding to block deinterleaving of a type B;

FIG. 365 is a block diagram showing another configuration example of the bit deinterleaver;

FIG. 366 is a block diagram showing a first configuration example of a reception system to which the reception apparatus can be applied;

FIG. 367 is a block diagram showing a second configuration example of the reception system to which the reception apparatus can be applied;

FIG. 368 is a block diagram showing a third configuration example of the reception system to which the reception apparatus can be applied; and

FIG. 369 is a block diagram showing a configuration example of an embodiment of a computer to which the present technology is applied.

DETAILED DESCRIPTION OF EMBODIMENTS 1. First Embodiment

Hereinafter, an embodiment of the present technology will be described, but an LDPC code will be described prior to the description.

LDPC Code

The LDPC code is a linear code, and is not necessarily a two-dimensional code. Here, it will be described that the LDPC code is a two-dimensional code.

The LDPC code has a greatest feature in that a parity check matrix which defines the LDPC code is a sparse matrix. Here, the sparse matrix refers to a matrix (matrix in which most of the elements are zero) in which the number of “1”s which are elements in a matrix is extremely small.

FIG. 1 is a diagram showing an example of a parity check matrix H of the LDPC code.

In the parity check matrix H of FIG. 1, a weight of each column (column weight) (the number of “1”s) is “3”, and a weight of each row (row weight) is “6”.

In the encoding (LDPC encoding) using the LDPC code, for example, a codeword (LDPC code) is generated by generating a generator matrix G based on the parity check matrix H and multiplying two-dimensional information bits by the generator matrix G.

Specifically, an encoding device that performs the LDPC encoding calculates the generator matrix G in which the expression GH^(T)=0 is established between a transposed matrix H_(T) of the parity check matrix H and the generator matrix. Here, when the generator matrix G is a K×N matrix, the encoding device generates an N-bit codeword c (=uG) by multiplying by the generator matrix G by a K-bit string (vector u) of the information bits. The codeword (LDPC code) generated by the encoding device is received by a reception side through a predetermined communication channel.

The LDPC code can be decoded by a message passing algorithm which is called probabilistic decoding suggested by Gallager and uses belief propagation on a so-called Tanner graph which includes a variable node (referred to as a message node) and a check node. Hereinafter, appropriately, the variable node and the check node are simply referred to as a node.

FIG. 2 is a flowchart showing a procedure of decoding the LDPC code.

Hereinafter, a real number value (reception LLR) obtained by representing the likelihood that the value of an i-th code bit of the LDPC code (one codeword) received by the reception side will be “0” using a log-likelihood ratio is appropriately referred to as a reception value u_(0i). A message output from the check node is represented as u_(j), and a message output from the variable node is represented as v_(i).

As shown in FIG. 2, in the decoding of the LDPC code, in step S11, after the LDPC code is received, the message (check node message) u_(j) is initialized by setting its value to “0”, a variable k expressed as an integer as a counter of an iteration process is initialized by setting its value to “0”, and the procedure proceeds to step S12. In step S12, the message (variable node message) v_(i) is obtained by performing a calculation (variable node calculation) represented by Expression (1) based on the reception value u_(0i) obtained by receiving the LDPC code, and the message u_(j) is obtained by performing a calculation (check node calculation) represented by Expression (2) based on the message v_(i).

$\begin{matrix} {v_{i} = {u_{0\; i} + {\sum\limits_{j = 1}^{d_{v} - 1}u_{j}}}} & (1) \\ {{\tanh \left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh \left( \frac{v_{i}}{2} \right)}}} & (2) \end{matrix}$

Where, d_(v) and d_(c) in Expression (1) and Expression (2) are respectively parameters, which indicate the number of “1”s in the longitudinal direction (column) and the transverse direction (row) of the parity check matrix H and can be arbitrarily selected. For example, in the case of the LDPC code ((3, 6) LDPC code) for the parity check matrix H shown in FIG. 1 in which the column weight is 3 and the row weight is 6, d_(v)=3, and d_(c)=6.

In the variable node calculation of Expression (1) and the check node calculation of Expression (2), since messages input from edges (lines connecting the variable node and the check node) to respectively output messages are not used as calculation targets, a calculation range is from 1 to d_(v)−1 or from 1 to d_(c)−1. A table of a function R(v₁, v₂) represented by Expression (3) defined by one output for two inputs v₁ and v₂ is created in advance, and the check node calculation of Expression (2) is performed by continuously (recursively) using the table as shown in Expression (4).

x=2 tan h ⁻¹{tan h(v ₁/2)tan h(v ₂/2)}=R(v ₁ ,v ₂)  (3)

u _(j) =R(v ₁ ,R(v ₂ ,R(v ₃ , . . . R(v _(d) _(c) ₋₂ ,v _(d) _(c) ₋₁))))  (4)

In step S12, the variable k is increased by “1”, and the procedure proceeds to step S13. In step S13, it is determined whether or not the variable k is greater than a predetermined iterative decoding number C. In step S13, when it is determined that the variable k is not greater than C, the procedure returns to step S12, and the same process is iterated.

In step S13, when it is determined that the variable k is greater than C, the procedure proceeds to step S14. Thereafter, the message v_(i) as a decoding result that is ultimately output is obtained by performing a calculation represented by Expression (5), and the obtained message is output. The decoding process of the LDPC code is ended.

$\begin{matrix} {v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v}}u_{j}}}} & (5) \end{matrix}$

Here, the calculation of Expression (5) is different from the variable node calculation of Expression (1), and is performed using the messages u_(j) from all edges that are connected to the variable node.

FIG. 3 is a diagram showing an example of the parity check matrix H of the (3, 6) LDPC code (a code rate of 1/2 and a code length of 12).

Similarly to FIG. 1, in the parity check matrix H of FIG. 3, the column weight is 3, and the row weight is 6.

FIG. 4 is a diagram showing the Tanner graph of the parity check matrix H of FIG. 3.

Here, in FIG. 4, nodes expressed as a plus “+” are check nodes, and nodes expressed as an equal sign “=” are variable nodes. The check nodes and the variable nodes correspond to the rows and columns of the parity check matrix H, respectively. Lines connecting the check nodes and the variable nodes are edges, and correspond to “1”s which are elements of the parity check matrix.

That is, when an element in the j-th row and the i-th column is 1, an i-th variable node (“=” node) from the top and a j-th check node (“+” node) from the top are connected through an edge in FIG. 4. The edge indicates that a code bit corresponding to the variable node has a constraint condition corresponding to the check node.

In a sum-product algorithm which is a method of decoding the LDPC code, the variable node calculation and the check node calculation are iteratively performed.

FIG. 5 is a diagram showing the variable node calculation performed in the variable node.

In the variable node, the message v_(i) corresponding to the edge to be calculated is obtained using the variable node calculation of Expression (1) using the reception value u_(0i) and the messages u₁ and u₂ from the remaining edges connected to the variable node. Messages corresponding to other edges are similarly obtained.

FIG. 6 is a diagram showing the check node calculation performed in the check node.

Here, the check node calculation of Expression (2) can be rewritten as Expression (6) by using a relationship of an expression a×b=exp{ln(|a|)+ln(|b|)}×sign(a)×sign(b). In this case, sign(x) is 1 when x≧0, and is −1 when x<0.

$\begin{matrix} \begin{matrix} {u_{j} = {2{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}}} \\ {= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {\sum\limits_{i = 1}^{d_{c} - 1}{\ln \left( {{\tanh \left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right\rbrack}}} \\ {= {2{\tanh^{- 1}\left\lbrack {\exp \left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}{- {\ln \left( {\tanh \left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}} \end{matrix} & (6) \end{matrix}$

In x≧0, when a function φ(x) is defined as the expression φ(x)=ln(tan h(x/2)), since the expression φ⁻¹(x)=2 tan h⁻¹(e^(−x)) is established, Expression (6) can be modified into Expression (7).

$\begin{matrix} {u_{j} = {{\varphi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}{\varphi \left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\left( v_{i} \right)}}}} & (7) \end{matrix}$

In the check node, the check node calculation of Expression (2) is performed according to Expression (7).

That is, as shown in FIG. 6, in the check node, the message u_(j) corresponding to the edge to be calculated is calculated by the check node calculation of Expression (7) using messages v₁, v₂, v₃, v₄ and v₅ from the remaining edges connected to the check node. Messages corresponding to other edges are similarly calculated.

The function φ(x) of Expression (7) can be expressed as the expression φ(x)=ln((e^(x)+1)/(e^(x)−1)), and when x>0, φ(x)=φ⁻¹(x). When the functions φ(x) and φ⁻¹(x) are implemented on hardware, these functions are implemented using a lookup table (LUT) in some cases, and the same LUT is used for both of these functions.

Configuration Example of Transmission System to which Present Technology is Applied

FIG. 7 is a diagram showing a configuration example of an embodiment of a transmission system (refers to a system in which a plurality of apparatuses is logically integrated irrespective of whether or not the respective apparatuses are present in the same housing) to which the present technology is applied.

In FIG. 7, the transmission system includes a transmission apparatus 11, and a reception apparatus 12.

The transmission apparatus 11 transmits (broadcasts) (sends), for example, television broadcasting programs. That is, the transmission apparatus 11 encodes, for example, target data which is a transmission target such as image data or voice data as the program into the LDPC code, and transmits the encoded code through a communication channel 13 such as a satellite channel, a terrestrial channel or a cable (wired channel).

The reception apparatus 12 receives the LDPC code transmitted from the transmission apparatus 11 through the communication channel 13, decodes the received code into the target data, and outputs the decoded data.

Here, it is understand that the LDPC code used in the transmission system of FIG. 7 exhibits extremely high capability in an additive white Gaussian noise (AWGN) communication channel.

Meanwhile, in the communication channel 13, a burst error or erasure may occur. For example, when the communication channel 13 is specifically a terrestrial channel, in an orthogonal frequency division multiplexing (OFDM) system, the power of a particular symbol may become zero (erasure) due to the delay of an echo (a path other than a main path) in a multi-path environment in which a desired-to-undesired (D/U) ratio is 0 dB (undesired=echo power is equal to desired=main path power).

Even in flutter (communication path in which the delay is zero and the echo to which the Doppler frequency is applied is added), when the D/U is 0 dB, the power of all OFDM symbols at a particular time may become zero (erasure) by the Doppler frequency.

A burst error may occur due to a state of a wiring from a reception unit (not shown) of the reception apparatus 12 such as an antenna that receives a signal from the transmission apparatus 11 to the reception apparatus 12 or instability of a power supply of the reception apparatus 12.

Meanwhile, in the decoding of the LDPC code, in the columns of the parity check matrix H and the variable nodes corresponding to the code bits of the LDPC code, since the variable node calculation of Expression (1) for performing the addition of (reception value u_(0i)) of the code bits of the LDPC code is performed as shown in FIG. 5, if the code bits used for the variable node calculation are in error, the accuracy of the obtained message is decreased.

In the decoding of the LDPC code, since the check node calculation of Expression (7) is performed in the check node by using the messages obtained in the variable nodes connected to the check node, when the number of check nodes in which errors (including erasure) simultaneously occur in (the code bits of the LDPC code corresponding to) the plurality of connected variable nodes is increased, decoding performance is degraded.

That is, for example, when the erasure simultaneously occurs in two or more variable nodes connected to the check node, the check node returns an equal-probability message in which a probability that the value will be zero and a probability that the value will be one are equal to each other to all of the variable nodes. In this case, the check node that returns the equal-probability message does not contribute to one decoding process (one set of the variable node calculation and the check node calculation), and thus, it is necessary to increase the number of times the decoding process is iterated. Accordingly, the decoding performance is degraded, and the power consumption of the reception apparatus 12 that decodes the LDPC code is increased.

Thus, in the transmission system of FIG. 7, it is possible to improve tolerance to the burst error or the erasure while maintaining performance in the AWGN communication channel (AWGN channel).

Configuration Example of Transmission Apparatus 11

FIG. 8 is a block diagram showing a configuration example of the transmission apparatus 11 of FIG. 7.

In the transmission apparatus 11, one or more input streams as target data are supplied to a mode adaptation/multiplexer 111.

The mode adaptation/multiplexer 111 performs a mode selection and a process such as multiplexing on one or more input streams being supplied thereto when necessary, and supplies data obtained as the result to a padder 112.

The padder 112 performs necessary zero padding (insertion of Nulls) on the data from the mode adaptation/multiplexer 111, and supplies data obtained as the result to a BB scrambler 113.

The BB scrambler 113 performs base-band (BB) scrambling on the data from the padder 112, and supplies data obtained as the result to a BCH encoder 114.

The BCH encoder 114 performs BCH encoding the data from the BB scrambler 113, and supplies data obtained as the processing result as LDPC target data which is an LDPC encoding target to an LDPC encoder 115.

The LDPC encoder 115 performs, for example, the LDPC encoding in accordance with the parity check matrix in which the parity matrix which is a part corresponding to the parity bits of the LDPC code has a dual diagonal structure on the LDPC target data from the BCH encoder 114, and outputs the LDPC code using the LDPC target data as the information bits.

That is, the LDPC encoder 115 performs the LDPC encoding that encodes the LDPC target data into the LDPC code (corresponding to the parity check matrix) defined by a predetermined standard such as DVB-S.2, DVB-T.2 or DVB-C.2, or the LDPC code (corresponding to the parity check matrix) to be adopted by ATSC 3.0, and outputs the LDPC code obtained as the result.

Here, the LDPC code defined by the DVB-T.2 standard or the LDPC code to be adopted by ATSC 3.0 is an irregular repeat-accumulate (IRA) code, and the parity matrix in the parity check matrix of the LDPC code has the dual diagonal structure. The parity matrix and the dual diagonal structure will be described below. The IRA code is described in, for example, “Irregular Repeat-Accumulate Codes,” H. Jin, A. Khandekar, and R. J. McEliece, in Proceedings of 2nd International Symposium on Turbo codes and Related Topics, pp. 1-8, September 2000.

The LDPC code output from the LDPC encoder 115 is supplied to a bit interleaver 116.

The bit interleaver 116 performs bit interleaving to be described below on the LDPC code from the LDPC encoder 115, and supplies the LDPC code on which the bit interleaving has been performed to a mapper 117.

The mapper 117 performs quadrature modulation (multi-level modulation) by mapping the LDPC code from the bit interleaver 116 to a signal point representing one symbol of the quadrature modulation for every one or more code bits of the LDPC code (for every symbol).

That is, the mapper 117 performs the quadrature modulation by mapping the LDPC code from the bit interleaver 116 to a signal point determined through a modulation scheme that performs the quadrature modulation of the LDPC code on an IQ plane (IQ constellation) defined using an I axis indicating an I component having the same phase as that of a carrier wave and a Q axis indicating a Q component perpendicular to the carrier wave.

When the number of signal points determined through the modulation scheme of the quadrature modulation performed by the mapper 117 is 2^(m), in the mapper 117, the LDPC code from the bit interleaver 116 is mapped to a signal point of 2^(m) number of signal points indicating a symbol for every symbol by using m number of code bits of the LDPC code as a symbol (one symbol).

Here, examples of the modulation scheme of the quadrature modulation performed by the mapper 117 include a modulation scheme defined by DVB-T.2, a modulation scheme to be adopted by ATSC 3.0, or other modulation schemes, that is, binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), 8 phase-shift keying (PSK), 16 amplitude and phase-shift keying (APSK), 32 APSK, 16 quadrature amplitude modulation (QAM), 64-QAM, 256-QAM, 1024-QAM, 4096-QAM and 4 pulse-amplitude modulation (PAM). In the mapper 117, whether to perform quadrature modulation of any modulation scheme is previously set depending on, for example, an operation input of an operator of the transmission apparatus 11.

The data (mapping result obtained by mapping the symbol to the signal point) obtained by the process in the mapper 117 is supplied to a time interleaver 118.

The time interleaver 118 performs time interleaving (interleaving in the time direction) on the data from the mapper 117 for every symbol, and supplies data obtained as the result to a single-input single-output/multiple-input single-output (SISO/MISO) encoder 119.

The SISO/MISO encoder 119 performs space-time encoding on the data from the time interleaver 118, and supplies the encoded data to a frequency interleaver 120.

The frequency interleaver 120 performs frequency interleaving (interleaving in the frequency direction) on the data from the SISO/MISO encoder 119 for every symbol, and supplies data to a frame builder and resource allocation unit 131.

Meanwhile, control data (signaling) for transmission control such as base-band (BB) signaling (BB header) is supplied to a BCH encoder 121.

Similarly to the BCH encoder 114, the BCH encoder 121 performs BCH encoding on the supplied control data, and supplies data obtained as the result to an LDPC encoder 122.

Similarly to the LDPC encoder 115, the LDPC encoder 122 performs LDPC encoding on the data from the BCH encoder 121 as LDPC target data, and supplies an LDPC code obtained as the result to a mapper 123.

Similarly to the mapper 117, the mapper 123 performs quadrature modulation by mapping the LDPC code from the LDPC encoder 122 for every one or more bits of the LDPC code (unit of the symbol) to a signal point indicating one symbol of the quadrature modulation, and supplies data obtained as the result to a frequency interleaver 124.

Similarly to the frequency interleaver 120, the frequency interleaver 124 performs frequency interleaving on the data from the mapper 123 for every symbol, and supplies data to the frame builder and resource allocation unit 131.

The frame builder and resource allocation unit 131 inserts pilot symbols into necessary positions of the data (symbol) from the frequency interleavers 120 and 124, constructs a frame (for example, a physical layer (PL) frame, a T2 frame, or a C2 frame) including a predetermined number of symbols from the data (symbol) obtained as the result, and supplies the constructed frame to an OFDM generation unit 132.

The OFDM generation unit 132 generates an OFDM signal corresponding to the frame, based on the frame from the frame builder and resource allocation unit 131, and transmits the generated signal through the communication channel 13 (FIG. 7).

The transmission apparatus 11 can be configured without including some of the blocks shown in FIG. 8 such as the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120 and the frequency interleaver 124.

Configuration Example of Bit Interleaver 116

FIG. 9 is a block diagram showing a configuration example of the bit interleaver 116 of FIG. 8.

The bit interleaver 116 has a function of interleaving data, and includes a parity interleaver 23, a group-wise interleaver 24, and a block interleaver 25.

The parity interleaver 23 performs parity interleaving that interleaves parity bits of the LDPC code from the LDPC encoder 115 into positions of other parity bits, and supplies the LDPC code on which the parity interleaving has been performed to the group-wise interleaver 24.

The group-wise interleaver 24 performs group-wise interleaving on the LDPC code from the parity interleaver 23, and supplies the LDPC code on which the group-wise interleaving has been performed to the block interleaver 25.

Here, in the group-wise interleaving, 360 bits of one group obtained by dividing the LDPC code corresponding to one code from a leading code thereof into a unit of 360 bits equal to a unit size P to be described below are grouped as a bit group, and the LDPC code from the parity interleaver 23 is interleaved for every bit group.

It is possible to further enhance an error rate when the group-wise interleaving is performed than when the group-wise interleaving is not performed. As a result, it is possible to ensure favorable communication quality in data transmission.

By performing block interleaving for demultiplexing the LDPC code from the group-wise interleaver 24, the block interleaver 25 symbolizes the LDPC code corresponding to one code into, for example, an m-bit symbol which is a unit of mapping, and the symbolized symbol is supplied to the mapper 117 (FIG. 8).

Here, in the block interleaving, the LDPC code from the group-wise interleaver 24 is written in a column (longitudinal) direction in a storage region in which columns as storage regions storing a predetermined number of bits in the column direction are arranged by the number corresponding to m number of bits of the symbol in a row direction (transverse direction), and is read in the row direction. Thus, the LDPC code corresponding to one code is symbolized into, for example, the m-bit symbol.

Parity Check Matrix of LDPC Code

FIG. 10 is a diagram showing an example of the parity check matrix H used for the LDPC encoding in the LDPC encoder 115 of FIG. 8.

The parity check matrix H has a low-density generator matrix (LDGM) structure, and can be expressed as the expression H=[H_(A)|H_(T)] (a matrix in which an element of an information matrix H_(A) is used as a left element, and an element of a parity matrix H_(T) is used as a right element) by the information matrix H_(A) which is a part corresponding to the information bits of the code bits of the LDPC code and the parity matrix H_(T) corresponding to the parity bits.

Here, the number of bits of the information bits of the code bits of the LDPC code (one codeword) of the one code and the number of bits of the parity bits are respectively referred to as an information length K and a parity length M, and the number of bits of the code bits of the LDPC code of one code (one codeword) is referred to as a code length N (=K+M).

The information length K and the parity length M of the LDPC code having a certain code length N are determined depending on a code rate. The parity check matrix H is a matrix in which row×column is M×N (matrix of M row×N column). The information matrix H_(A) is an M×K matrix, and the parity matrix H_(T) is an M×M matrix.

FIG. 11 is a diagram showing an example of the parity matrix H_(T) of the parity check matrix H used for the LDPC encoding in the LDPC encoder 115 of FIG. 8.

The parity matrix H_(T) of the parity check matrix H used for the LDPC encoding in the LDPC encoder 115 is the same as the parity matrix H_(T) of the parity check matrix H of the LDPC code defined by the standard such as DVB-T.2.

As shown in FIG. 11, the parity matrix H_(T) of the parity check matrix H of the LDPC code defined by the standard such as DVB-T.2 is a matrix having a dual diagonal structure (lower bidiagonal matrix) in which the elements of 1s are arranged in a so-called dual diagonal form. The row weight of the parity matrix H_(T) is 1 for the first row, and is 2 for all of the remaining rows. The column weight is 1 for the last column, and is 2 for all of the remaining columns.

As mentioned above, the LDPC code of the parity check matrix H of which the parity matrix H_(T) has the dual diagonal structure can be generated using the parity check matrix H.

That is, the LDPC code (one codeword) is expressed as a row vector c, and a column vector which is the transpose of the row vector is expressed as c^(T). A part of the information bits of the row vector c which is the LDPC code is expressed as a row vector A, and a part of the parity bits is expressed as a row vector T.

In this case, the row vector c can be expressed as the express c=[A|T] (row vector in which an element of the row vector A is used as a left element and an element of the row vector T is used as a right element) by the row vector A as the information bits and the row vector T as the parity bits.

The parity check matrix H and the row vector c=[A|T] as the LDPC code are necessary to satisfy the expression Hc^(T)=0, and when the parity matrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has the dual diagonal structure shown in FIG. 11, the row vector T as the parity bits constituting the row vector c=[A|T] that satisfies the expression Hc^(T)=0 can be successively (sequentially) calculated by sequentially changing the elements of the respective rows to zero from the first element of the column vector Hc^(T) in the expression Hc^(T)=0.

FIG. 12 is a diagram showing the parity check matrix H of the LDPC code defined by the standard such as DVB-T.2.

The column weight of a KX column from the first column of the parity check matrix H of the LDPC code defined by the standard such as DVB-T.2 is X, the column weight of the K3 column is 3, the column weight of the M−1 column is 2, and the column weight of the last column is 1.

Here, KX+K3+M−1+1 is equal to the code length N.

FIG. 13 is a diagram showing column numbers KX, K3 and M and a column weight X with respect to the respective code rates r of the LDPC code defined by the standard such as DVB-T.2.

In the standard such as DVB-T.2, the LDPC codes having the code lengths N of 64,800 bits and 16,200 bits are defined.

Eleven code rates (nominal rates) of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10 are defined for the LDPC code having the code length N of 64,800 bits, and ten code rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9 are defined for the LDPC code having the code length N of 16,200 bits.

Here, the code length N of 64,800 bits is referred to as 64 k bits, and the code length N of 16,200 bits is referred to as 16 k bits.

In the case of the LDPC code, code bits of the parity check matrix H corresponding to columns having a larger column weight tend to have lower error rates.

In the parity check matrix H defined by the standard such as DVB-T.2 shown in FIGS. 12 and 13, the column weight of the column on the leading side (the left side) tends to be large, and thus, in the case of the LDPC code corresponding to the parity check matrix H, the first code bit tends to have high error tolerance (has tolerance to an error), and the last code bit tends to have low error tolerance.

Parity Interleaving

The parity interleaving performed by the parity interleaver 23 of FIG. 9 will be described with reference to FIGS. 14 to 16.

FIG. 14 is a diagram showing an example of (a part of) the Tanner graph of the parity check matrix of the LDPC code.

As shown in FIG. 14, when errors such as erasure simultaneously occur in (code bits corresponding to) the plurality of variable nodes such as two variable nodes connected to the check node, the check node returns the equal-probability message in which the probability that the value will be zero and the probability that the value will be one are equal to all of the variable nodes connected to the check node. Thus, when the erasure simultaneously occurs in the plurality of variable nodes connected to the same check node, the decoding performance is degraded.

However, the LDPC code output from the LDPC encoder 115 of FIG. 8 is an IRA code similarly to the LDPC code defined by the standard such as DVB-T.2, and the parity matrix H_(T) of the parity check matrix H has the dual diagonal structure as shown in FIG. 11.

FIGS. 15A and 15B are diagrams showing examples of the parity matrix H_(T) having the dual diagonal structure as shown in FIG. 11 and the Tanner graph corresponding to the parity matrix H_(T).

FIG. 15A shows an example of the parity matrix H_(T) having the dual diagonal structure, and FIG. 15B shows the Tanner graph corresponding to the parity matrix H_(T) of FIG. 15A.

In the parity matrix H_(T) having the dual diagonal structure, the elements of “1”s are adjacent to each other in the respective rows (except for the first column). For this reason, in the Tanner graph of the parity matrix H_(T), two adjacent variable nodes corresponding to columns of two adjacent elements in which the values of the parity matrix H_(T) are 1s are connected to the same check node.

Accordingly, when the parity bits corresponding to the two adjacent variable nodes are simultaneously in error due to the burst error or the erasure, since the check node connected to the two variable nodes (variable nodes requesting messages using the parity bits) corresponding to the two parity bits in error returns the equal-probability message in which the probability that the value will be zero and the probability that the value will be one are equal to the variable nodes connected to the check node, the decoding performance is degraded. When a burst length (the number of bits of the parity bits that are continuously in error) is increased, the number of check nodes that return the equal-probability message is increased, and thus, the decoding performance is further degraded.

Thus, in order to prevent the degradation of the decoding performance, the parity interleaver 23 (FIG. 9) performs the parity interleaving that interleaves the parity bits of the LDPC code from the LDPC encoder 115 into positions of other parity bits.

FIG. 16 is a diagram showing the parity matrix H_(T) of the parity check matrix H corresponding to the LDPC code on which the parity interleaving has been performed by the parity interleaver 23 of FIG. 9.

Here, the information matrix H_(A) of the parity check matrix H corresponding to the LDPC code output from the LDPC encoder 115 has a cyclic structure similarly to the information matrix of the parity check matrix H corresponding to the LDPC code defined by the standard such as DVB-T.2.

The cyclic structure refers to a structure in which a certain column coincides with a column obtained by performing cyclic shifting on another column, and includes, for example, a structure in which the positions of 1s of the respective rows of the P column for each of the P columns are positions obtained by performing cyclic-shifting in the column direction by a predetermined value such as a value proportional to a value q obtained by dividing the first column of the P column by the parity length M. Hereinafter, the P column in the cyclic structure is appropriately referred to as a unit size.

As described in FIGS. 12 and 13, as the LDPC code defined by the standard of DVB-T.2, there are two types of LDPC codes of which the code lengths N are 64,800 bits and 16,200 bits, and the unit size P of both of these two types of LDPC codes is defined as 360 which is one of divisors except for 1 and M of divisors of the parity length M.

Further, the parity length M is a value other than a prime number represented by the expression M=q×P=q×360 by using the value q different depending on the code rate. Accordingly, similarly to the unit size P, the value q is another one of the divisors except for 1 and M of the divisors of the parity length M, and is obtained by dividing the parity length M by the unit size P (the product of P and q which are divisors of the parity length M is the parity length M).

As described above, when the information length is K, an integer which is 0 or greater and less than P is x, an integer which is 0 or greater and less than q is y, the parity interleaver 23 interleaves the (K+qx+y+1)-th code bit of the code bits of the N-bit LDPC code into the position of the (K+Py+x+1)-th code bit.

Since both of the (K+qx+y+1)-th code bit and the (K+Py+x+1)-th code bit are code bits subsequent to a (K+1)-th code bit, these bits are parity bits. Accordingly, the positions of the parity bits of the LDPC code are moved through the parity interleaving.

According to the parity interleaving, since (the parity bits corresponding to) the variable nodes connected to the same check node are separated by the unit size P, that is, 360 bits, when the burst length is less than 360 bits, it is possible to avoid the situation that the plurality of variable nodes connected to the same check node are simultaneously in error, and as a result, it is possible to improve tolerance to the burst error.

The LDPC code on which the parity interleaving that interleaves the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit has been performed coincides with the LDPC code (hereinafter, referred to as a permutation parity check matrix) of the parity check matrix obtained by performing column permutation that permutes the (K+qx+y+1)-th column of the original parity check matrix H into the (K+Py+x+1)-th column.

As shown in FIG. 16, a pseudo-cyclic structure having the P columns (360 columns in FIG. 16) as a unit appears in the parity matrix of the permutation parity check matrix.

Here, the pseudo-cyclic structure refers to a structure in which parts except for a part have the cyclic structure.

The permutation parity check matrix obtained by performing the column permutation corresponding to the parity interleaving on the parity check matrix of the LDPC code defined by the standard such as DVB-T.2 is a so-called pseudo-cyclic structure not the (complete) cyclic structure in which the number of the elements of 1s is short by one (the element of 1 becomes the element of 0) in a part of 360 rows×360 columns (shift matrix to be described below) which is an upper-right corner part of the permutation parity check matrix.

Similarly to the permutation parity check matrix for the parity check matrix of the LDPC code defined by the standard such as DVB-T.2, the permutation parity check matrix for the parity check matrix of the LDPC code output from the LDPC encoder 115 has, for example, the pseudo-cyclic structure.

The permutation parity check matrix of FIG. 16 is a matrix on which the permutation of rows (row permutation) has performed on the original parity check matrix H in order to allow the permutation parity check matrix to be constructed as constitutive matrices to be described below in addition to the column permutation corresponding to the parity interleaving.

FIG. 17 is a flowchart for describing a process performed in the LDPC encoder 115, the bit interleaver 116 and the mapper 117 of FIG. 8.

The LDPC encoder 115 waits for the LDPC target data to be supplied from the BCH encoder 114, encodes the LDPC target data into the LDPC code in step S101, and supplies the LDPC code to the bit interleaver 116. The process proceeds to step S102.

In step S102, the bit interleaver 116 performs the bit interleaving on the LDPC code from the LDPC encoder 115, and supplies a symbol obtained by performing the bit interleaving to the mapper 117. The process proceeds to step S103.

That is, in step S102, the parity interleaver 23 of the bit interleaver 116 (FIG. 9) performs the parity interleaving on the LDPC code from the LDPC encoder 115, and supplies the LDPC code on which the parity interleaving has been performed to the group-wise interleaver 24.

The group-wise interleaver 24 performs the group-wise interleaving on the LDPC code from the parity interleaver 23, and supplies the LDPC code to the block interleaver 25.

The block interleaver 25 performs the block interleaving on the LDPC code on which the group-wise interleaving has been performed by the group-wise interleaver 24, and supplies an m-bit symbol obtained as the result to the mapper 117.

In step S103, the mapper 117 performs the quadrature modulation by mapping the symbol from the block interleaver 25 to any one of 2^(m) number of signal points determined through the modulation scheme of the quadrature modulation performed by the mapper 117, and supplies data obtained as the result to the time interleaver 118.

As stated above, it is possible to improve the error rate when the plurality of code bits of the LDPC code is transmitted as one symbol by performing the parity interleaving and the group-wise interleaving.

Here, for the sake of convenience in the description, although it has been described in FIG. 9 that the parity interleaver 23 which is the block that performs the parity interleaving and the group-wise interleaver 24 which is the block that performs the group-wise interleaving are individually provided, the parity interleaver 23 and the group-wise interleaver 24 may be integrally configured.

That is, both of the parity interleaver and the group-wise interleaving can be performed by writing and reading the code bits in and from the memory, and can be expressed by a matrix for converting an address (write address) where the code bits are written into an address (read address) where the code bits are read.

Accordingly, if a matrix obtained by multiplying a matrix representing the parity interleaving and a matrix representing the group-wise interleaving is obtained, the code bits are converted by using these matrices. Therefore, it is possible to obtain the result on which the parity interleaving is performed and the group-wise interleaving is performed on the LDPC code on which the parity interleaving has been performed.

It is possible to integrally configure the block interleaver 25 in addition to the parity interleaver 23 and the group-wise interleaver 24.

That is, the block interleaving performed in the block interleaver 25 can also be expressed by a matrix for converting a write address where the LDPC code is stored into a read address.

Accordingly, if a matrix obtained by multiplying the matrix representing the parity interleaving, the matrix representing the group-wise interleaving and the matrix representing the block interleaving is obtained, it is possible to collectively perform the parity interleaving, the group-wise interleaving and the block interleaving by using these matrices.

Configuration Example of LDPC Encoder 115

FIG. 18 is a block diagram showing a configuration example of the LDPC encoder 115 of FIG. 8.

The LDPC encoder 122 of FIG. 8 also has the same configuration.

As described in FIGS. 12 and 13, in the standard such as DVB-T.2, two types of LDPC codes having the code lengths N of 64,800 bits and 16,200 bits are defined.

Eleven code rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9 and 9/10 are defined for the LDPC code having the code length N of 64,800 bits, and tens code rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6 and 8/9 are defined for the LDPC code having the code length N of 16,200 bits (FIGS. 12 and 13).

For example, the LDPC encoder 115 can perform encoding (error-correction encoding) using the LDPC codes of the respective code rates which have the code lengths N of 64,800 bits and 16,200 bits according to the parity check matrix H provided for each the code lengths N and each code rate.

The LDPC encoder 115 includes an encoding unit 601, and a storage unit 602.

The encoding unit 601 includes a code rate setting module 611, an initial value table reading module 612, a parity check matrix generating module 613, an information bit reading module 614, an encoding parity calculating module 615, and a control module 616. The encoding unit performs the LDPC encoding on the LDPC target data supplied to the LDPC encoder 115, and supplies the LDPC code obtained as the result to the bit interleaver 116 (FIG. 8).

That is, the code rate setting module 611 sets the code length N and the code rate of the LDPC code depending on, for example, an operation input of the operator.

The initial value table reading module 612 reads a parity check matrix initial value table to be described below, which corresponds to the code length N and the code rate set by the code rate setting module 611, from the storage unit 602.

The parity check matrix generating module 613 generates the parity check matrix H by arranging the elements of 1s of the information matrix H_(A) corresponding to the information length K (=code length N−parity length M) according to the code rate and the code length N set by the code rate setting module 611 for every 360 columns (unit size P) in the column direction based on the parity check matrix initial value table read by the initial value table reading module 612, and stores the generated parity check matrix in the storage unit 602.

The information bit reading module 614 reads (extracts) the information bits having the information length K from the LDPC target data supplied to the LDPC encoder 115.

The encoding parity calculating module 615 reads the parity check matrix H generated by the parity check matrix generating module 613 from the storage unit 602, and generates the codeword (LDPC code) by calculating the parity bits with respect to the information bits read by the information bit reading module 614 based on the predetermined expression by using the parity check matrix H.

The control module 616 controls the respective blocks constituting the encoding unit 601.

For example, a plurality of parity check matrix initial value tables corresponding to the plurality of code rates shown in FIGS. 12 and 13 for the code lengths N of 64,800 bits and 16,200 bits is stored in the storage unit 602. The storage unit 602 temporarily stores necessary data in the process of the encoding unit 601.

FIG. 19 is a flowchart for describing an example of the process of the LDPC encoder 115 of FIG. 18.

In step S201, the code rate setting module 611 determines (sets) the code length N and the code rate r for performing the LDPC encoding.

In step S202, the initial value table reading module 612 reads a predetermined parity check matrix initial value table corresponding to the code length N and the code rate r determined by the code rate setting module 611 from the storage unit 602.

In step S203, the parity check matrix generating module 613 obtains (generates) the parity check matrix H of the LDPC code having the code length N and the code rate r determined by the code rate setting module 611 by using the parity check matrix initial value table read from the storage unit 602 by the initial value table reading module 612, and stores the obtained parity check matrix in the storage unit 602.

In step S204, the information bit reading module 614 reads the information bits having the information length K (=N×r) corresponding to the code length N and the code rate r determined by the code rate setting module 611 from the LDPC target data supplied to the LDPC encoder 115, reads the parity check matrix H obtained by the parity check matrix generating module 613 from the storage unit 602, and supplies the read information bits and the parity check matrix to the encoding parity calculating module 615.

In step S205, the encoding parity calculating module 615 calculates the parity bits of the codeword c satisfying Expression (8) by using the parity check matrix H and the information bits from the information bit reading module 614.

Hc ^(T)=0  (8)

In Expression (8), c represents a row vector as the codeword (LDPC code), and c^(T) represents the transpose of the row vector c.

Here, as stated above, a part of the information bits of the row vector c as the LDPC code (one codeword) is represented as a row vector A, and when a part of the parity bits is represented by a row vector T, the row vector c can be expressed by the expression c=[A|T] by using the row vector A as the information bits and the row vector T as the parity bits.

When the parity matrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has the dual diagonal structure shown in FIG. 11, the parity check matrix H and the row vector c=[A|T] as the LDPC code are necessary to satisfy the expression Hc^(T)=0, and the row vector T as the parity bits constituting the row vector c=[A|T] satisfying the expression Hc^(T)=0 can be sequentially obtained by sequentially converting the elements of the respective rows into zero from the elements of the first row of the column vector Hc^(T) in the expression Hc^(T)=0.

The encoding parity calculating module 615 obtains the parity bits T for the information bits A from the information bit reading module 614, and outputs the codeword c=[A|T] expressed by the information bits A and the parity bits T as the result of the LDPC encoding of the information bits A.

Thereafter, in step S206, the control module 616 determines whether or not the LDPC encoding has ended. In step S206, when it is determined that the LDPC encoding has not ended, that is, when, for example, the LDPC target data to be subject to the LDPC encoding is still present, the process returns to step S201 (or step S204), and thereinafter, the processes of step S201 (or step S204) to step S206 are repeated.

In step S206, when it is determined that the LDPC encoding has ended, that is, when, for example, the LDPC target data to be subject to the LDPC encoding is not present, the LDPC encoder 115 ends the process.

As mentioned above, the parity check matrix initial value table corresponding to the code rates r and the code lengths N is provided, and the LDPC encoder 115 performs the LDPC encoding with a predetermined code length N and a predetermined cord rate r by using the parity check matrix H generated from the parity check matrix initial value table corresponding to the predetermined code length N and the predetermined code rate r.

Example of Parity Check Matrix Initial Value Table

The parity check matrix initial value table is a table in which the positions of the elements of 1s of the information matrix H_(A) (FIG. 10) of the parity check matrix H corresponding to the information length K depending on the code rate r and the code length N of the LDPC code (LDPC code defined by the parity check matrix H) are represented for every 360 columns (unit size P), and is previously created for each parity check matrix H of each code length N and each code rate r.

That is, in the parity check matrix initial value table, at least the positions of the elements of 1s of the information matrix H_(A) are represented for every 360 columns (unit size P).

As the parity check matrix H, there are a parity check matrix which is defined by DVB-T.2 and in which (all of) the parity matrices H_(T) have the dual diagonal structure, and a parity check matrix which is suggested by CRC/ETRI and in which a part of the parity matrix H_(T) has the dual diagonal structure and the remaining part has a diagonal matrix (unit matrix).

Hereinafter, an expression method of a parity check matrix initial value table representing the parity check matrix which is defined by DVB-T.2 and in which the parity matrix H_(T) has the dual diagonal structure is referred to as a DVB method, and an expression method of a parity check matrix initial value table representing the parity check matrix suggested by CRC/ETRI is referred to as a ETRI method.

FIG. 20 is a diagram showing an example of the parity check matrix initial value table of the DVB method.

That is, FIG. 20 shows a parity check matrix initial value table for a parity check matrix H which is defined by the standard of DVB-T.2 and has a code length N of 16,200 bits and a code rate (code rate described in DVB-T.2) r of 1/4.

The parity check matrix generating module 613 (FIG. 18) obtains the parity check matrix H by using the parity check matrix initial value table of the DVB method as will be described below.

FIG. 21 is a diagram for describing a method of obtaining the parity check matrix H from the parity check matrix initial value table of the DVB method.

That is, FIG. 21 is a parity check matrix initial value table for a parity check matrix H which is defined by the standard of DVB-T.2 and has a code length N of 16,200 bits and a code rate r of 2/3.

The parity check matrix initial value table of the DVB method is a table in which the positions of all of the elements of 1s of the information matrix H_(A) corresponding to the information length K in accordance with the code rate r and the code length N of the LDPC code are represented for every 360 columns (unit size P), and row numbers of the elements of 1s of the (1+360×(i−1))-th column of the parity check matrix H (row numbers in which a row number of the first row of the parity check matrix H is zero) are arranged in the i-th row by the number of a column weight of the (1+360×(i−1))-th column.

Here, since the parity check matrix H_(T) (FIG. 10) of the parity check matrix H of the DVB method corresponding to the parity length M is determined to have the dual diagonal structure as shown in FIG. 15, if the information matrix H_(A) (FIG. 10) corresponding to the information length K can be obtained using the parity check matrix initial value table, it is possible to obtain the parity check matrix H.

A row number k+1 of the parity check matrix initial value table of the DVB method is different depending on the information length K.

The relationship of Expression (9) is established between the information length K and the row number k+1 of the parity check matrix initial value table.

K=(k+1)×360  (9)

Here, 360 of Expression (9) is the unit size P described in FIG. 16.

In the parity check matrix initial value table of FIG. 21, thirteen values are arranged from the first row to the third row, and three values are arranged from the fourth row to the (k+1)-th row (30th row in FIG. 21).

Accordingly, the column weight of the parity check matrix H obtained from the parity check matrix initial value table of FIG. 21 is 13 from the first column to the (1+360×(3−1)−1)-th column, and is 3 from the (1+360×(3−1))-th column to the K-th column.

The first row of the parity check matrix initial value table of FIG. 21 is 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622, and this means that the elements of the rows having row numbers of 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622 are 1s (and other elements are 0s) in the first column of parity check matrix H.

The second row of the parity check matrix initial value table of FIG. 21 is 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108, and this means that the elements of the rows having row numbers of 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108 are 1s in the (361(=1+360×(2−1)))-th row of the parity check matrix H.

As stated above, in the parity check matrix initial value table, the positions of the elements of 1s of the information matrix H_(A) of the parity check matrix H are represented for every 360 columns.

Columns other than the (1+360×(i−1))-th column of the parity check matrix H, that is, the respective columns from the (2+360×(i−1))-th column to the (360×i)-th column are arranged by periodically cyclic-shifting the elements of 1s of the (1+360×(i−1))-th column determined by the parity check matrix initial value table in the lower direction (lower direction of the columns) according to the parity length M.

That is, for example, the (2+360×(i−1))-th column is obtained by cyclic-shifting the (1+360×(i−1))-th column in the lower direction by M/360(=q), and the next (3+360×(i−1))-th column is obtained by cyclic-shifting ((2+360×(i−1))-th column obtained by cyclic-shifting the (1+360×(i−1))-th column in the lower direction by 2×M/360(=2×q) in the lower direction by M/360(=q).

When the value of the j-th column (the j-th column from the left) of the i-th row (i-th row from the top) of the parity check matrix initial value table is represented as h_(i, j), and a row number of a j-th element of 1 of the w-th column of the parity check matrix H is represented as H_(w-j), the row number H_(w-j) of the element of 1 of the w-th column which is a column other than the (1+360×(i−1))-th column of the parity check matrix H can be obtained using Expression (10).

H _(w-j)=mod {h _(i,j)+mod((w−1),P)×q,M)  (10)

Where, mod(x, y) means a remainder obtained by dividing x by y.

In the first embodiment, P is the aforementioned unit size, and is 360 as in the standard of, for example, DVB-S.2, DVB-T.2 and DVB-C.2. Furthermore, q is a value of M/360 obtained by dividing the parity length M by the unit size P (=360).

The parity check matrix generating module 613 (FIG. 18) specifies the row number of the element of 1 of the (1+360×(i−1))-th column of the parity check matrix H by using the parity check matrix initial value table.

Moreover, the parity check matrix generating module 613 (FIG. 18) obtains the row number H_(w-j) of the element of 1 of the w-th column which is the column other than the (1+360×(i−1))-th column of the parity check matrix H according to Expression (10), and the parity check matrix H having the element of 1 of the row number as obtained above is generated.

FIG. 22 is a diagram showing the structure of the parity check matrix of the ETRI method.

The parity check matrix of the ETRI method includes an A matrix, a B matrix, a C matrix, a D matrix, and a Z matrix.

The A matrix is a matrix on an upper left side of the parity check matrix which is expressed as information length K of LDPC code=code length N×code rate r and a predetermined value g and has g rows and k columns.

The B matrix is a matrix which has g rows and g columns and has a dual diagonal structure which is adjacent to a right side of the A matrix.

The C matrix is a matrix which has N−K−g rows and K+g columns and is adjacent to a lower side of the A matrix and the B matrix.

The D matrix is a unit matrix which has N−K−g rows and N−K−g columns and is adjacent to a right side of the C matrix.

The Z matrix is a zero matrix (0 matrix) which has g rows and N−K−g columns and is adjacent to a right side of the B matrix.

In the parity check matrix of the ETRI method including the A matrix to the D matrix and the Z matrix described above, a part of the A matrix and the C matrix constitutes the information matrix, and the remaining part of the B matrix and the C matrix, the D matrix and the Z matrix constitute the parity matrix.

Since the B matrix is the matrix having the dual diagonal structure and the D matrix is the unit matrix, a part (a part of the B matrix) of the parity matrix of the parity check matrix of the ETRI method has the dual diagonal structure, and the remaining part thereof (a part of the D matrix) is the diagonal matrix (unit matrix).

Similarly to the information matrix of the parity check matrix of the DVB method, the A matrix and the C matrix have the cyclic structure for every 360 columns (unit size P), and in the parity check matrix initial value table of the ETRI method, the positions of the elements of 1s of the A matrix and the C matrix are represented for every 360 columns.

Here, as described above, since a part of the A matrix and the C matrix constitutes the information matrix, in the parity check matrix initial value table of the ETRI method in which the positions of the elements of 1s of the A matrix and the C matrix are represented for every 360 columns, at least the positions of the elements of 1s of the information matrix can be represented for every 360 columns.

FIG. 23 is a diagram showing an example of the parity check matrix initial value table of the ETRI method.

That is, FIG. 23 shows an example of the parity check matrix initial value table for the parity check matrix having a code length N of 50 bits and a code rate r of 1/2.

The parity check matrix initial value table of the ETRI method is a table in which the positions of the elements of 1s of the A matrix and the C matrix are represented for each unit size P, and the row numbers of the elements of 1s of the (1+P×(i−1))-th column of the parity check matrix (the row numbers in which the row numbers of the first row of the parity check matrix are 0s) are arranged in the i-th column by the column weight of the columns of the (1+P×(i−1))-th column.

Here, for the sake of convenience in the description, the unit size P is, for example, 5.

As parameters of the parity check matrix of the ETRI method, there are g=M₁, M₂, Q₁, and Q₂.

g=M₁ is a parameter for determining the size of the B matrix, and is a value of a multiple of the unit size P. When the performance of the LDPC code is changed by adjusting g=M₁ and the parity check matrix is determined, a predetermined value is adjusted. Here, it is assumed that g=M₁, and the unit size P=5 multiplied by 3=15.

M₂ is a value M−M₁ which is the parity length M minus M₁.

Here, since the information length K is N×r=50×1/2=25 and the parity length M is N−K=50−25=25, M₂ is M−M₁=25−15=10.

Q₁ is obtained according to the expression Q₁=M₁/P, and represents the number of shifts (the number of rows) in the cyclic shifting in the A matrix.

That is, the columns other than the (1+P×(i−1))-th column of the A matrix of the parity check matrix of the ETRI method, that is, the respective columns from the (2+P×(i−1))-th column to the (P×i)-th column are arranged by periodically cyclic-shifting the elements of 1s of the (1+360×(i−1))-th columns determined by the parity check matrix initial value table in the lower direction (lower direction of the columns), and Q₁ represents the number of shifts in the cyclic shifting in the A matrix.

Q₂ is obtained according to the expression Q₂=M₂/P, and represents the number of shifts (the number of rows) in the cyclic shifting in the C matrix.

That is, the columns other than the (1+P×(i−1))-th column of the C matrix of the parity check matrix of the ETRI method, that is, the respective columns from the (2+P×(i−1))-th column to the (P×i)-th column are arranged by periodically cyclic-shifting the elements of 1s of the (1+360×(i−1))-th column determined by the parity check matrix initial value table in the lower direction (lower direction of the columns), and Q₂ represents the number of shifts in the cyclic shifting in the C matrix.

Here, Q₁ is M₁/P=15/5=3, and Q₂ is M₂/P=10/5=2.

In the parity check matrix initial value table of FIG. 23, three values are arranged in the first row and the second row, and one value is arranged from the third row to the fifth row. According to the arrangement of these values, the column weight of the parity check matrix obtained from the parity check matrix initial value table of FIG. 23 is 3 from the first column to the (1+5×(2−1)-1)-th column, and is 1 from the (1+5×(2−1))-th column to the fifth column.

That is, the first row of the parity check matrix initial value table of FIG. 23 is 2, 6, and 18, and this means that the elements of the respective rows having the row numbers of 2, 6, and 18 are 1s (and other elements are 0s) in the first column of the parity check matrix.

In this case, since the A matrix is a matrix in 15 rows and 25 columns (g rows and K columns) and the C matrix is the matrix in 10 rows and 40 columns (N−K−g rows and K+g columns), the rows having row numbers of 0 to 14 of the parity check matrix are the rows of the A matrix, and the rows having row numbers of 15 to 24 of the parity check matrix are rows of the C matrix.

Accordingly, among the rows having the row numbers of 2, 6 and 18 (hereinafter, described as the rows #2, #6, and #18), the rows #2 and #6 are the rows of the A matrix, and the row #18 is the row of the C matrix.

The second row of the parity check matrix initial value table of FIG. 23 is 2, 10, and 19, and this means that the elements of the rows #2, #10, and #19 are 1s in the 6(=1+5×(2−1))-th column of the parity check matrix.

Here, the rows #2 and #10 of the rows #2, #10, and #19 in the 6(=1+5×(2−1))-th column of the parity check matrix are the rows of the A matrix, and the row #19 is the row of the C matrix.

The third row of the parity check matrix initial value table of FIG. 23 is 22, and this means that the elements of the row #22 in the 11(=1+5×(3−1))-th row of the parity check matrix are 1s.

Here, the row #22 in the 11(=1+5×(3−1))-th row of the parity check matrix is the row of the C matrix.

Similarly, 19 of the fourth row of the parity check matrix initial value table of FIG. 23 means that the elements of the row #19 in the 16(=1+5×(4-1))-th column of the parity check matrix are 1s, and 15 of the fifth row of the parity check matrix initial value table of FIG. 23 means that the elements of the row #15 in the 21(=1+5×(5-1))-th column are 1s.

As stated above, in the parity check matrix initial value table, the positions of the elements of 1s of the A matrix and the C matrix of the parity check matrix are represented for each unit size P=5.

The columns other than the (1+5×(i−1))-th column of the A matrix and the C matrix of the parity check matrix, that is, the respective columns from the (2+5×(i−1))-th column to the (5×i)-th column are arranged by periodically cyclic-shifting the elements of 1s of the (1+5×(i−1))-th columns determined by the parity check matrix initial value table in the lower direction (lower direction of the columns) according to the parameters Q₁ and Q₂.

That is, for example, the (2+5×(i−1))-th column of the A matrix is obtained by cyclic-shifting the (1+5×(i−1))-th column in the lower direction by Q₁(=3), and the next (3+5×(i−1))-th column is obtained by cyclic-shifting the (2+5×(i−1))-th column obtained by cyclic shifting the (1+5×(i−1))-th column in the lower direction by 2×Q₁(=2×3) in the lower direction by Q₁.

For example, the (2+5×(i−1))-th column of the C matrix is obtained by cyclic-shifting the (1+5×(i−1))-th column in the lower direction by Q₂(=2), and the next (3+5×(i−1))-th column is obtained by cyclic-shifting the (2+5×(i−1))-th column obtained by cyclic-shifting the (1+5×(i−1))-th column in the lower direction by 2×Q₂(=2×2) in the lower direction by Q₂.

FIG. 24 is a diagram showing the A matrix generated from the parity check matrix initial value table of FIG. 23.

In the A matrix of FIG. 24, according to the first row of the parity check matrix initial value table of FIG. 23, the elements of the rows #2 and #6 of the 1(=1+5×(1−1))-st column are 1s.

Moreover, the respective columns from the 2(=2+5×(1−1))-nd column to the 5(=5+5×(1−1))-th column are obtained by cyclic-shifting the immediately previous columns in the lower direction by Q₁=3.

In the A matrix of FIG. 24, according to the second row of the parity check matrix initial value table of FIG. 23, the elements of the rows #2 and #10 of the 6(=1+5×(2−1))-th column are 1s.

The respective columns from the 7(=2+5×(2−1))-th column to the 10(=5+5×(2−1))-th column are obtained by cyclic-shifting the immediately previous columns in the lower direction by Q₁=3.

FIG. 25 is a diagram showing the parity interleaving on the B matrix.

The parity check matrix generating module 613 (FIG. 18) generates the A matrix by using the parity check matrix initial value table, and arranges the B matrix having the dual diagonal structure so as to be adjacent to the right side of the A matrix. The parity check matrix generating module 613 regards the B matrix as the parity matrix, and performs the parity interleaving such that the adjacent elements of 1s of the B matrix having the dual diagonal structure are separated from each other by the unit size P=5 in the row direction.

FIG. 25 shows the B matrix and the A matrix on which the parity interleaving has been performed on the B matrix.

FIG. 26 is a diagram showing the C matrix generated from the parity check matrix initial value table of FIG. 23.

In the C matrix of FIG. 26, according to the first row of the parity check matrix initial value table of FIG. 23, the elements of the row #18 of the 1(=1+5×(1−1))-st column of the parity check matrix are 1s.

The respective columns from the 2(=2+5×(1−1))-nd column to the 5(=5+5×(1−1))-th column of the C matrix are obtained by cyclic-shifting the immediately previous columns in the lower direction by Q₂=2.

In the C matrix of FIG. 26, according to the second row to the fifth row of the parity check matrix initial value table of FIG. 23, the elements of the row #19 of the 6(=1+5×(2−1))-th column of the parity check matrix, the row #22 of the 11(=1+5×(3−1))-th column, the row #19 of the 16(=1+5×(4−1))-th column, and the row #15 of the 21(=1+5×(5−1))-st column are 1s.

The respective columns from the 7(=2+5×(2−1))-th column to the 10(=5+5×(2−1))-th column, the respective columns from the 12(=2+5×(3−1))-th column to the 15(=5+5×(3−1))-th column, the respective columns from the 17(=2+5×(4−1))-th column to the 20(=5+5×(4−1))-th column, and the respective columns from the 22(=2+5×(5−1))-nd column to the 25(=5+5×(5−1))-th column are obtained by cyclic shifting the immediately previous columns in the lower direction by Q₂=2.

The parity check matrix generating module 613 (FIG. 18) generates the C matrix by using the parity check matrix initial value table, and arranges the C matrix under the A matrix and the B matrix (on which the parity interleaving has been performed).

Further, the parity check matrix generating module 613 arranges the Z matrix so as to be adjacent to the right side of the B matrix, arranges the D matrix to be adjacent to the right side of the C matrix, and generates the parity check matrix shown in FIG. 26.

FIG. 27 is a diagram showing the parity interleaving on the D matrix.

After the parity check matrix of FIG. 26 is generated, the parity check matrix generating module 613 regards the D matrix as the parity matrix, and performs the parity interleaving on only the D matrix such that the elements of 1s of the odd-number rows and the next even-number rows of the D matrix of the unit matrix are separated from each other by the unit size P=5.

FIG. 27 shows the parity check matrix on which the parity interleaving has been performed on the D matrix for the parity check matrix of FIG. 26.

(The encoding parity calculating module 615 (FIG. 18) of) the LDPC encoder 115 performs the LDPC encoding (generates the LDPC code) by using, for example, the parity check matrix of FIG. 27.

Here, the LDPC code generated using the parity check matrix of FIG. 27 is the LDPC code on which the parity interleaving has been performed, and thus, it is not necessary to perform the parity interleaving on the LDPC code generated using the parity check matrix of FIG. 27 in the parity interleaver 23 (FIG. 9).

FIG. 28 is a diagram showing a parity check matrix obtained by performing the column permutation as the parity interleaving that returns the parity interleaving to the original state on the B matrix, a part of the C matrix (a part of the C matrix which is arranged under the B matrix) and the D matrix of the parity check matrix of FIG. 27.

In the LDPC encoder 115, it is possible to perform the LDPC encoding (generate the LDPC code) by using the parity check matrix of FIG. 28.

When the LDPC encoding is performed using the parity check matrix of FIG. 28, the LDPC code on which the parity interleaving has not been performed is obtained according to the LDPC encoding. Accordingly, when the LDPC encoding is performed using the parity check matrix of FIG. 28, the parity interleaving is performed in the parity interleaver 23 (FIG. 9).

FIG. 29 is a diagram showing a transformation check matrix obtained by performing the row permutation on the parity check matrix of FIG. 27.

As will be described below, the transformation check matrix is a matrix represented by combining a unit matrix of P×P, a quasi-unit matrix in which one or more 1s of 1s of the unit matrix are 0s, a shift matrix obtained by cyclic-shifting the unit matrix or the quasi-unit matrix, a sum matrix which is the sum of two or more matrices of the unit matrix, the quasi-unit matrix and the shift matrix, and a 0 matrix of P×P.

By using the transformation check matrix in the decoding of the LDPC code, it is possible to adopt an architecture in which the check node calculation and the variable node calculation are simultaneously performed P times in the decoding of the LDPC code, as will be described below.

New LDPC Code

The standard of the terrestrial digital television broadcasting called ATSC 3.0 is currently being developed.

Now, a renewed LDPC code (hereinafter, referred to as a new LDPC code) capable of being used in data transmission other than ATSC 3.0 will be described.

For example, as the new LDPC code, it is possible to adopt the LDPC code of the ETRI method or the LDPC code of the DVB method which has the unit size P of 360 which is the same as that of DVB-T.2, and corresponds to the parity check matrix having the cyclic structure.

The LDPC encoder 115 (FIG. 8 and FIG. 18) can perform the LDPC encoding on the new LDPC code by using the parity check matrix obtained from the parity check matrix initial value table of the new LDPC code having a code length N of 16 k bits or 64 k bits and a code rate r of any one of 5/15, 6, 15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15.

In this case, the parity check matrix initial value table of the new LDPC code is stored in the storage unit 602 of the LDPC encoder 115 (FIG. 8).

FIG. 30 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (16 k, 8/15)) which has a code length N of 16 k bits and a code rate r of 8/15 and is suggested by the present applicant.

FIG. 31 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (16 k, 10/15)) which has a code length N of 16 k bits and a code rate r of 10/15 and is suggested by the present applicant.

FIG. 32 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (16 k, 12/15)) which has a code length N of 16 k bits and a code rate r of 12/15 and is suggested by the present applicant.

FIGS. 33, 34 and 35 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (64 k, 7/15)) which has a code length N of 64 k bits and a code rate of 7/15 and is suggested by the present applicant.

FIG. 34 is a drawing subsequent to FIG. 33, and FIG. 35 is a drawing subsequent to FIG. 34.

FIGS. 36, 37 and 38 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (64 k, 9/15)) which has a code length N of 64 k bits and a code rate r of 9/15 and is suggested by the present applicant.

FIG. 37 is a drawing subsequent to FIG. 36, and FIG. 38 is a drawing subsequent to FIG. 37.

FIGS. 39, 40, 41 and 42 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (64 k, 11/15)) which has a code length N of 64 k bits and a code rate r of 11/15 and is suggested by the present applicant.

FIG. 40 is a drawing subsequent to FIG. 39, FIG. 41 is a drawing subsequent to FIG. 40, and FIG. 42 is a drawing subsequent to FIG. 41.

FIGS. 43, 44, 45 and 46 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a Sony code of (64 k, 13/15)) which has a code length N of 64 k bits and a code rate r of 13/15 and is suggested by the present applicant.

FIG. 44 is a drawing subsequent to FIG. 43, FIG. 45 is a drawing subsequent to FIG. 44, and FIG. 46 is a drawing subsequent to FIG. 45.

FIGS. 47 and 48 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a Samsung code of (64 k, 6/15)) which has a code length N of 64 k bits and a code rate r of 6/15 and is suggested by Samsung Electronics Co., Ltd.

FIG. 48 is a drawing subsequent to FIG. 47.

FIGS. 49, 50 and 51 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a Samsung code of (64 k, 8/15)) which has a code length N of 64 k bits and a code rate r of 8/15 and is suggested by Samsung Electronics Co., Ltd.

FIG. 50 is a drawing subsequent to FIG. 49, and FIG. 51 is a drawing subsequent to FIG. 50.

FIGS. 52, 53 and 54 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a Samsung code of (64 k, 12/15)) which has a code length N of 64 k bits and a code rate r of 12/15 and is suggested by Samsung Electronics Co., Ltd.

FIG. 53 is a drawing subsequent to FIG. 52, and FIG. 54 is a drawing subsequent to FIG. 53.

FIG. 55 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, referred to as a LGE code of (16 k, 6/15)) which has a code length N of 16 k bits and a code rate r of 6/15 and is suggested by LGE Inc.

FIG. 56 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a LGE code O (16 k, 7/15)) which has a code length N of 16 k bits and a code rate r of 7/15 and is suggested by LGE Inc.

FIG. 57 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a LGE code of (16 k, 9/15)) which has a code length N of 16 k bits and a code rate r of 9/15 and is suggested by LGE Inc.

FIG. 58 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a LGE code of (16 k, 11/15)) which has a code length N of 16 k bits and a code rate r of 11/15 and is suggested by LGE Inc.

FIG. 59 is a diagram showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a LGE code of (16 k, 13/15)) which has a code length N of 16 k bits and a code rate r of 13/15 and is suggested by LGE Inc.

FIGS. 60, 61 and 62 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a LGE code of (64 k, 10/15)) which has a code length N of 64 k bits and a code rate r of 10/15 and is suggested by LGE Inc.

FIG. 61 is a drawing subsequent to FIG. 60, and FIG. 62 is a drawing subsequent to FIG. 61.

FIGS. 63, 64 and 65 are diagrams showing an example of the parity check matrix initial value table of the DVB method for the parity check matrix of the new LDPC code (hereinafter, a NERC code of (64 k, 9/15)) which has a code length N of 64 k bits and a code rate r of 9/15 and is suggested by the NERC.

FIG. 64 is a drawing subsequent to FIG. 63, and FIG. 65 is a drawing subsequent to FIG. 64.

FIG. 66 is a diagram showing an example of the parity check matrix initial value table of the ETRI method for the parity check matrix of the new LDPC code (hereinafter, a ETRI code of (16 k, 5/15)) which has a code length N of 16 k bits and a code rate r of 5/15 and is suggested by CRC/ETRI.

FIGS. 67 and 68 are diagrams showing an example of the parity check matrix initial value table of the ETRI method for the parity check matrix of the new LDPC code (hereinafter, referred to as a ETRI code of (64 k, 5/15)) which has a code length N of 64 k bits and a code rate r of 5/15 and is suggested by CRC/ETRI.

FIG. 68 is a drawing subsequent to FIG. 67.

FIGS. 69 and 70 are diagrams showing an example of the parity check matrix initial value table of the ETRI method for the parity check matrix of the new LDPC code (hereinafter, referred to as a ETRI code of (64 k, 6/15)) which has a code length N of 64 k bits and a code rate r of 6/15 and is suggested by CRC/ETRI.

FIG. 70 is a drawing subsequent to FIG. 69.

FIGS. 71 and 72 are diagrams showing an example of the parity check matrix initial value table of the ETRI method for the parity check matrix of the new LDPC code (hereinafter, referred to as a ETRI code of (64 k, 7/15)) which has a code length N of 64 k bits and a code rate r of 7/15 and is suggested by CRC/ETRI.

FIG. 72 is a drawing subsequent to FIG. 71.

Among the new LDPC codes, particularly, the Sony codes are LDPC codes having good performance.

Here, the LDPC codes having good performance are LDPC codes obtained from an appropriate parity check matrix H.

For example, the appropriate parity check matrix H is a parity check matrix which has a smaller BER (bit error rate) (and FER (frame error rate)) and satisfies a predetermined condition when the LDPC code obtained from the parity check matrix H is transmitted with a low E_(s)/N₀ or E_(b)/N_(o) (the ratio of the signal power to the noise power per one bit).

It is possible to obtain the appropriate parity check matrix H by performing, for example, a simulation that measures a BER when the LDPC codes obtained from various parity check matrices satisfying a predetermined condition are transmitted with a low E_(s)/N_(o).

As the predetermined conditions to be satisfied by the appropriate parity check matrix H, there are a condition in which an analysis result obtained by a code performance analysis method called density evolution is favorable and a condition in which a loop of the elements of 1s called cycle-4 is not present.

In the information matrix H_(A), when the elements of 1s are concentrated as in cycle-4, it is considered that the decoding performance of the LDPC code is degraded, and thus, a condition in which cycle-4 is not present is necessary as the predetermined condition to be satisfied by the appropriate parity check matrix H.

It is possible to appropriately determine the predetermined condition to be satisfied by the appropriate parity check matrix H in order to improve the decoding performance of the LDPC code or easily perform (simplify) the decoding process of the LDPC code.

FIGS. 73 and 74 are diagrams for describing the density evolution that obtains the analysis result as the predetermined condition to be satisfied by the appropriate parity check matrix H.

The density evolution is a code analysis method of calculating an expectation value of an error probability of an ensemble of LDPC codes which is specified by a degree sequence to be described below and has a code length N of ∞.

For example, when the variance of noise is steadily increased from zero on an AWGN channel, an expectation value of an error possibility of a certain ensemble is initially zero, but when the variance of noise is equal to or greater than a certain threshold, the expectation value thereof does not become zero.

According to the density evolution, it is possible to determine if the performance of the ensemble is good or bad (appropriateness of the parity check matrix) by comparing the expectation value with a threshold (hereinafter, referred to as a performance threshold) of the variance of noise in which the expectation value of the error probability does not become zero.

With regard to a specific LDPC code, when an ensemble to which the LDPC code belongs is determined and the density evolution is performed, it is possible to roughly predict performance of the LDPC code.

Accordingly, if the ensemble having good performance is found, it is possible to find the LDPC code having good performance from the LDPC codes belonging to the ensemble.

Here, the aforementioned degree sequence means what percentage of the variable nodes or the check nodes having the respective weight values are present in the LDPC code having the code length N.

For example, a regular (3, 6) LDPC code having a code rate of 1/2 belongs to an ensemble specified by the degree sequence in which the weights (column weights) of all variable nodes are 3 and the weights (row weights) of all check nodes are 6.

FIG. 73 shows a Tanner graph of such an ensemble.

In the Tanner graph of FIG. 73, variable nodes shown by a circle (O mark) in the drawing are present by an N number equal to the code length N, and check nodes shown by a square (square mark) in the drawing are present by a N/2 number equal to a multiplication value obtained by multiplying the code length N by the code rate of 1/2.

Three edges equal to the column weight are connected to the respective variable nodes, and thus, edges connected to the N number of variable nodes are present by a 3N number in total.

Six edges equal to the row weight are connected to the respective check nodes, and thus, edges connected to N/2 number of check nodes are present by a 3N number in total.

Furthermore, in the Tanner graph of FIG. 73, one interleaver is present.

The interleaver randomly rearranges 3N number of edges connected to N number of variable nodes, and connects the rearranged edges to any one of 3N number of edges connected to N/2 number of check nodes.

As a rearrangement pattern in which 3N number of edges connected to N number of variable nodes are rearranged in the interleaver, there are (3N)!(=(3N)×(3N−1)× . . . ×1) number of methods. Accordingly, an ensemble specified by the degree sequence in which the weights of all variable nodes are 3 and the weights of all check nodes are 6 is a set of (3N)! number of LDPC codes.

In the simulation for obtaining the LDPC code (appropriate parity check matrix) having good performance, a multi-edge type ensemble is used in the density evolution.

In the multi-edge type, the interleaver through which the edges connected to the variable nodes and the edges connected to the check nodes pass is divided into multiple edges, and thus, the ensemble is more precisely specified.

FIG. 74 shows an example of the Tanner graph of the multi-edge type ensemble.

In the Tanner graph of FIG. 74, two interleavers including a first interleaver and a second interleaver are present.

In the Tanner graph of FIG. 74, v1 number of variable nodes of which one edge is connected to the first interleaver and no edges are connected to the second interleaver, and v2 number of variable nodes of which one edge is connected to the first interleaver and two edges are connected to the second interleaver, and v3 number of variable nodes of which no edges are connected to the first interleaver and two edges are connected to the second interleaver are presented.

In the Tanner graph of FIG. 74, c1 number of check nodes of which two edges are connected to the first interleaver and no edges are connected to the second interleaver, c2 number of check nodes of which two edges are connected to the first interleaver and two edges are connected to the second interleaver, and c3 number of check nodes of which no edges are connected to the first interleaver and three edges are connected to the second interleaver are present.

The density evolution and the implementation thereof are described in, for example, “On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit”, S. Y. Chung, G. D. Forney, T. J. Richardson, R. Urbanke, IEEE Communications Leggers, VOL. 5, NO. 2, February 2001.

In the simulation for obtaining (the parity check matrix initial value table of) the Sony codes, an ensemble of which a performance threshold which is E_(b)/N₀ (ratio of signal power to noise power per one bit) at which a BER starts to be decreased (become smaller) is equal to or less than a predetermined value is found through the multi-edge type density evolution, and the LDPC code capable of reducing the BER when one or more quadrature modulation schemes such as QPSK are used is selected as the LDPC code having good performance from the LDPC codes belonging to the found ensemble.

The parity check matrix initial value table of the Sony codes is obtained through the simulation described above.

Therefore, according to the Sony codes obtained from the parity check matrix initial value table, it is possible to ensure favorable communication quality in data transmission.

FIG. 75 is a diagram for describing the parity check matrices H (hereinafter, described as “parity check matrices H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15)”) obtained from the parity check matrix initial value table of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

All minimum cycle lengths of the parity check matrix H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) exceed the cycle-4, and thus, the cycle-4 (a loop of the elements of 1s which has a loop length of 4) is not present. Here, the minimum cycle length (girth) means the minimum value of the length of the loop (loop length) constructed by the elements of 1s of the parity check matrix H.

A performance threshold of the Sony code of (16 k, 8/15) is 0.805765, a performance threshold of the Sony code of (16 k, 10/15) is 2.471011, and a performance threshold of the Sony code of (16 k, 12/15) is 4.269922.

In the parity check matrix H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), column weights from the first column to the KX1-th column are X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th column is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=16,200 bits of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) are shown in FIG. 75.

Similarly to the parity check matrix described in FIGS. 12 and 13, in the parity check matrix H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), the column weight of the column on the leading side (on the left side) tends to be large, and thus, the code bits of the Sony code on the leading side tend to have high error tolerance (have tolerance to an error).

According to the simulation performed by the present applicant, favorable BER/FER are obtained for the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), and thus, it is possible to ensure favorable communication quality in data transmission using the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

FIG. 76 is a diagram for describing the parity check matrix H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

All minimum cycle lengths of the parity check matrix H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15) exceed the cycle-4, and thus, the cycle-4 is not present.

A performance threshold of the Sony code of (64 k, 7/15) is −0.093751, a performance threshold of the Sony code of (64 k, 9/15) is 1.658523, a performance threshold of the Sony code of (64 k, 11/15) is 3.351930, and a performance threshold of the Sony code of (64 k, 13/15) is 5.301749.

In the parity check matrix H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15), column weights from the first column to the KX1-th column are X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th column is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64,800 bits of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15) are shown in FIG. 76.

Similarly to the parity check matrix described in FIGS. 12 and 13, in the parity check matrix H of the Sony code of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15), the column weight of the column on the leading side (on the left side) tends to be large, and thus, the code bits of the Sony code on the leading side tend to have high error tolerance.

According to the simulation performed by the present applicant, favorable BER/FER are obtained for the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15), and thus, it is possible to ensure favorable communication quality in data transmission using the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

FIG. 77 is a diagram for describing the parity check matrix H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15).

In the parity check matrix H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15), column weights from the first column to the KX1-th column are X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64,800 bits of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15) are shown in FIG. 77.

FIG. 78 is a diagram for describing the parity check matrix H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15).

In the parity check matrix H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15), column weights from the first column to the KX1-th column are X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th column is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=16,200 bits of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15) are shown in FIG. 78.

FIG. 79 is a diagram for describing the parity check matrix H of the LGE code of (64 k, 10/15).

In the parity check matrix H of the LGE code of (64 k, 10/15), a column weight from the first column to the KX1-th column is X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64,800 bits of the LGE code of (64 k, 10/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the LGE code of (64 k, 10/15) are shown in FIG. 79.

FIG. 80 is a diagram for describing the parity check matrix H of the NERC code of (64 k, 9/15).

In the parity check matrix H of the NERC code of (64 k, 9/15), column weights from the first column to the KX1-th column are X1, a column weight of the KX2-th column is X2, a column weight of the KY1-th column is Y1, a column weight of the KY2-th column is Y2, a column weight of the (M−1)-th column is 2, and a column weight of the last column is 1.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64,800 bits of the NERC code of (64 k, 9/15).

The column numbers KX1, KX2, KY1, KY2, and M and the column weights X1, X2, Y1, and Y2 of the parity check matrix H of the NERC code of (64 k, 9/15) are shown in FIG. 80.

FIG. 81 is a diagram for describing the parity check matrix H of the ETRI code of (16 k, 5/15).

In the parity check matrix H of the ETRI code of (16 k, 5/15), a parameter g=M₁ is 720.

Since the ETRI code of (16 k, 5/15) has a code length N of 16,200 and a code rate r of 5/15, an information length K=N×r is 16,200×5/15=5,400, and a parity length M=N−K is 16,200−5,400=10,800.

A parameter M₂=M−M₁=N−K−g is 10,800−720=10,080.

Accordingly, a parameter Q₁=M₁/P is 720/360=2, and a parameter Q₂=M₂/P is 10,080/360=28.

FIG. 82 is a diagram for describing the parity check matrix H of the ETRI codes of (64 k, 5/15), (64 k, 6/15), and (64 k, 7/15).

Parameters g=M₁, M₂/Q₁ and Q₂ for the parity check matrix H of the ETRI codes of (64 k, 5/15), (64 k, 6/15), and (64 k, 7/15) are shown in FIG. 82.

Constellation

FIGS. 83 to 104 are diagrams showing an example of the type of a constellation adopted by the transmission system of FIG. 7.

For example, in the transmission system of FIG. 7, it is possible to set a constellation to be used in MODCOD to the MODCOD which is a combination of the modulation scheme and the LDPC code.

That is, in the transmission system of FIG. 7, the LDPC code is classified into nine types of LDPC codes having code rates r of 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15 according to the code rate r (regardless of the code length N), and combinations of these nine types of LDPC codes (the LDPC codes having code rates r of 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) and the respective modulation schemes can be adopted as the MODCOD.

In the transmission system of FIG. 7, it is possible to set one or more constellations to be used in one MODCOD modulation scheme to the MODCOD.

As the constellation, there are a uniform constellation (UC) in which signal points are uniformly arranged, and a non-uniform constellation (NUC) in which signal points are not uniformly arranged.

As the NUC, for example, there is a constellation called a 1-dimensional M²-QAM non-uniform constellation (1D NUC) and a constellation called a 2-dimensional QQAM non-uniform constellation (2D NUC).

In general, the 1D NUC can improve a BER further than the UC, and the 2D NUC can improve a BER further than the 1D NUC.

The constellation of the QPSK modulation scheme is the UC. As the constellation of the 16-QAM, 64-QAM or 256-QAM modulation scheme, it is possible to adopt, for example, the 2D NUC, and as the constellation of the 1024-QAM or 4096-QAM modulation scheme, it is possible to adopt, for example, the 1D NUC.

Hereinafter, the NUC constellation used in the MODCOD in which the modulation scheme is a modulation scheme of mapping a m-bit symbol to any one of 2^(m) number of signal points and the code rate of the LDPC code is r is described as a NUC_2^(m)_r.

For example, “NUC_16_6/15” refers to the NUC constellation used in the MODCOD in which the modulation scheme is a 16-QAM modulation scheme (in addition, a modulation scheme of mapping a symbol to any one of 16 signal points) and the code rate r of the LDPC code is 6/15.

In the transmission system of FIG. 7, when the modulation scheme is QPSK, the same constellation is used for the respective code rates r of the LDPC code.

In the transmission system of FIG. 7, when the modulation scheme is 16-QAM, 64-QAM or 256-QAM, different 2D NUC constellations are used for the code rates r of the LDPC code.

Moreover, in the transmission system of FIG. 7, when the modulation scheme is 1024-QAM or 4096-QAM, different 1D NUC constellations are used for the code rates r of the LDPC code.

Accordingly, as described above, when the LDPC code is classified into nine types of LDPC codes having r=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, 13/15 according to the code rate r, one type of constellation is provided for QPSK, nine types of 2D NUC constellations are provided for 16-QAM, 64-QAM and 256-QAM, and nine types of 1D NUC constellations are provided for 1024-QAM and 4096-QAM.

FIG. 83 is a diagram showing examples of the 2D NUC constellations for the nine types of LDPC codes having the code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) when the modulation scheme is 16-QAM.

FIG. 84 is a diagram showing examples of the 2D NUC constellations for the nine types of LDPC codes having the code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) when the modulation scheme is 64-QAM.

FIG. 85 is a diagram showing examples of the 2D NUC constellations for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC codes when the modulation scheme is 256-QAM.

FIG. 86 is a diagram showing examples of the 1D NUC constellations for the nine types of LDPC codes having the code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) when the modulation scheme is 1024-QAM.

FIGS. 87 and 88 are diagrams showing examples of the 1D NUC constellations for the nine types of LDPC codes having the code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) when the modulation scheme is 4096-QAM.

In FIGS. 83 to 88, a horizontal axis and a vertical axis are respectively an I axis and a Q axis, and Re{x₁} and Im{x₁} are respectively a real part and an imaginary part of a signal point x₁, as a coordinate of the signal point x₁.

In FIGS. 83 to 88, a value described before “for CR” represents the code rate r of the LDPC code.

FIG. 89 is a diagram showing an example of the coordinate of the signal point of the UC that is commonly used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is QPSK.

In FIG. 89, “Input cell word y” represents a 2-bit symbol mapped to the UC of QPSK, and “Constellation point z_(q)” represents the coordinate of a signal point z_(q). The index q of the signal point z_(q) represents a discrete time of a symbol (a time interval between a given symbol and the next symbol).

In FIG. 89, the coordinate of the signal point z_(q) is represented in the form of a complex number, and i represents an imaginary unit (√(−1)).

FIG. 90 is diagram showing an example of the coordinate of the signal point of the 2D NUC of FIG. 83 used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is 16-QAM.

FIG. 91 is diagram showing an example of the coordinate of the signal point of the 2D NUC of FIG. 84 used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is 64-QAM.

FIGS. 92 and 93 are diagrams showing an example of the coordinate of the signal point of the 2D NUC of FIG. 85 used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is 256-QAM.

In FIGS. 90 to 93, NUC_2^(m)_r represents the coordinate of the signal point of the 2D NUC used when the modulation scheme is 2^(m)-QAM and the code rate of the LDPC code is r.

Similarly to FIG. 89, in FIGS. 90 to 93, the coordinate of the signal point z_(q) is represented in the form of a complex number, and i represents an imaginary unit.

In FIGS. 90 to 93, w#k represents the coordinate of a signal point in a first quadrant of the constellation.

In the 2D NUC, a signal point in a second quadrant of the constellation is disposed in a position where the signal point in the first quadrant is symmetrically moved with respect to the Q axis, and a signal point in a third quadrant of the constellation is disposed in a position where the signal point in the first quadrant is symmetrically moved with respect to an origin. A signal point in a fourth quadrant of the constellation is disposed in a position where the signal point in the first quadrant is symmetrically moved with respect to the I axis.

Here, when the modulation scheme is 2^(m)-QAM, m bits are used as one symbol, and the one symbol is mapped to a signal corresponding to the symbol.

The m-bit symbol is represented as, for example, an integer value of 0 to 2^(m)−1. However, when b=2m/4, symbols y(0), y(1), . . . , and y(2^(m)−1) that are expressed as integer values of 0 to 2^(m)−1 can be classified into four symbols including symbols y(0) to y(b−1), y(b) to y(2b−1), y(2b) to y(3b−1), and y(3b) to y(4b−1).

In FIGS. 90 to 93, the suffix k in w#k is represented as an integer value in a range of 0 to b−1, and w#k represents the coordinate of a signal point corresponding to a symbol y(k) in a range of symbols y(0) to y(b−1).

The coordinate of a signal point corresponding to a symbol y(k+b) in a range of symbols y(b) to y(2b−1) is represented as −conj(w#k), the coordinate of a signal point corresponding to a symbol y(k+2b) in a range of symbols y(2b) to y(3b−1) is represented as conj(w#k), and the coordinate of a signal point corresponding to a symbol y(k+3b) in a range of symbols y(3b) to y(4b−1) is represented as −w#k.

Here, conj(w#k) represents complex conjugates of w#k.

For example, when the modulation scheme is 16-QAM, symbols y(0), y(1), . . . , and y(15) of m=4 bits are classified into four symbols including symbols y(0) to y(3), y(4) to y(7), y(8) to y(11) and y(12) to y(15) since b=2⁴/4=4.

Furthermore, for example, since the symbol y(12) of the symbols y(0) to y(15) is a symbol y(k+3b)=y(0+3×4) in a range of symbols y(3b) to y(4b−1) and k=0, the coordinate of a signal point of the symbol y(12) is −w#k=−w0.

When the code rate r of the LDPC code is, for example, 9/15, since w0 (NUC_16_9/15) when the modulation scheme is 16-QAM and the code rate r is 9/15 is 0.4967+1.1932i according to FIG. 90, the coordinate −w0 of the signal point corresponding to the symbol y(12) is −(0.4967+1.1932i).

FIG. 94 is a diagram showing an example of the coordinate of the signal point of the 1D NUC of FIG. 86 used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is 1024-QAM.

In FIG. 94, rows of NUC_1 k_r represent values of u#k representing the coordinate of the signal point of the 1D NUC used when the modulation scheme is 1024-QAM and the code rate of the LDPC code is r.

u#k represents a real part Re(z_(q)) and an imaginary part Im(z_(q)) of a complex number as the coordinate of the signal point z_(q) of the 1D NUC.

FIG. 95 is a diagram showing the relationship between a symbol y of 1024-QAM and u#k as the real part Re(z_(q)) and the imaginary part Im(z_(q)) of the complex number representing the coordinate of the signal point z_(q) of the 1D NUC corresponding to the symbol y.

It is assumed that a 10-bit symbol y of 1024-QAM is represents as y_(0, q), y_(1, q), y_(2, q), y_(3, q), y_(4, q), y_(5, q), y_(6, q), y_(7, q), y_(8, q), y_(9, q) from the leading bit (most significant bit).

FIG. 95A shows the correspondence relationship between five odd-numbered bits y_(0, q), y_(2, q), y_(4, q), y_(6, q), y_(8, q) of the symbol y and u#k representing the real part Re(z_(q)) of (the coordinate of) the signal point z_(q) corresponding to the symbol y.

FIG. 95B shows the correspondence relationship between five even-numbered bits y_(1, q), y_(3, q), y_(5, q), y_(7, q), y_(9, q) of the symbol y and u#k representing the imaginary part Im(z_(q)) of (the coordinate of) the signal point z_(q) corresponding to the symbol y.

When the 10-bit symbol y=(y_(0, q), y_(1, q), y_(2, q), y_(3, q), y_(4, q), y_(5, q), y_(6, q), y_(7, q), y_(8, q), y_(9, q)) of 1024-QAM is, for example, (0, 0, 1, 0, 0, 1, 1, 1, 0, 0), five odd-numbered bits (y_(0, q), y_(2, q), y_(4, q), y_(6, q), y_(8, q)) are (0, 1, 0, 1, 0), and five even-numbered bits (y_(1, q), y_(3, q), y_(5, q), y_(7, q), y_(9, q)) are (0, 0, 1, 1, 0).

In FIG. 95A, the five odd-numbered bits (0, 1, 0, 1, 0) correspond to u3, and thus, the real part Re(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) corresponds to u3.

Moreover, in FIG. 95B, the five even-numbered bits (0, 0, 1, 1, 0) correspond to u11, and thus, the imaginary part Im(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u11.

Meanwhile, when it is assumed that the code rate r of the LDPC code is, for example, 7/15, u3 of the 1D NUC(NUC_1 k_7/15) used when the modulation scheme is 1024-QAM and the code rate r of the LDPC code is 7/15 is 1.1963, and u11 is 6.9391 according to FIG. 94 described above.

Accordingly, the real part Re(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u3=1.1963, and Im(z_(q)) is u11=6.9391. As a result, the coordinate of a signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is represented as 1.1963+6.9391i.

FIG. 96 is a diagram showing an example of the coordinate of the signal point of the 1D NUC of FIGS. 87 and 88 used for the nine types of code rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of the LDPC code when the modulation scheme is 4096-QAM.

In FIG. 96, the respective rows represent values of u#k representing the coordinate of the signal point of the 1D NUC used when the modulation scheme is 4096-QAM and the code rates of the LDPC code are r=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15.

u#k represents a real part Re(z_(q)) and an imaginary part Im(z_(q)) of a complex number as the coordinate of the signal point z_(q) of the 1D NUC.

FIGS. 97A and 97B are diagrams showing the relationship between the symbol y of 4096-QAM and u#k as the real part Re(z_(q)) and the imaginary part Im(z_(q)) of the complex number representing the coordinate of the signal point z_(q) of the 1D NUC corresponding to the symbol y.

Since a method of obtaining the coordinate of the signal point of the 1D NUC of 4096-QAM using FIGS. 96 and 97 is the same as the method of obtaining the coordinate of the signal point of the 1D NUC of 1024-QAM using FIGS. 94 and 95, the description thereof will be omitted.

FIG. 98 is a diagram showing another example of the constellation of the 2D NUC for the nine types of code rates of the LDPC code when the modulation scheme is 16-QAM.

FIG. 99 is a diagram showing another example of the constellation of the 2D NUC for the nine types of code rates of the LDPC code when the modulation scheme is 64-QAM.

FIG. 100 is a diagram showing another example of the constellation of the 2D NUC for the nine types of code rates of the LDPC code when the modulation scheme is 256-QAM.

Similarly to FIGS. 83 to 88, in FIGS. 98 to 100, a horizontal axis and a vertical axis are respectively an I axis and a Q axis, and Re{x₁} and Im{x₁} represent a real part and an imaginary part of a signal point x₁ as the coordinate of the signal point x₁. In FIGS. 98 to 100, values described before “for CR” represent the code rates r of the LDPC code.

FIG. 101 is a diagram showing an example of the coordinate of the signal point of the 2D NUC of FIG. 98 used for the nine types of code rates of the LDPC code when the modulation scheme is 16-QAM.

FIG. 102 is a diagram showing an example of the coordinate of the signal point of the 2D NUC of FIG. 99 used for the nine types of code rates of the LDPC code when the modulation scheme is 64-QAM.

FIGS. 103 and 104 are diagrams showing an example of the coordinate of the signal point of the 2D NUC of FIG. 100 used for the nine types of code rates of the LDPC code when the modulation scheme is 256-QAM.

In FIGS. 101 to 104, NUC_2^(m)_r represents the coordinate of the signal point of the 2D NUC used when the modulation scheme is 2^(m)_QAM and the code rate of the LDPC code is r, similarly to FIGS. 90 to 93.

The signal points of the 1D NUC are arranged in a straight line parallel to the I axis or a straight line parallel to the Q axis in a lattice shape. An interval between the signal points is not uniform. When (data mapped to) the signal points is transmitted, an average power of the signal point on the constellation is normalized. When it is assumed that a root-mean-square value of an absolute value of (coordinates of) all signal points on the constellation is represented as P_(ave), the normalization is performed by multiplying the reciprocal 1/(√P_(ave)) of the respective signal points z_(q) on the constellation by the square root √P_(ave) the root-mean-square value P_(ave).

According to the constellations described in FIGS. 83 to 104, it can be seen that a favorable error rate is obtained.

Block Interleaver 25

FIG. 105 is a block diagram showing a configuration example of the block interleaver 25 of FIG. 9.

The block interleaver 25 includes a storage region called a part 1, and a storage region called a part 2.

Both of the parts 1 and 2 are configured in such a manner that columns as storage regions that store one bit in a row (transverse) direction and store a predetermined number of bits in a column (longitudinal) direction are arranged by a number C equal to m which is the number of bits of a symbol in the row direction.

When it is assumed that the number of bits (hereinafter, referred to as a part column length) stored in the column direction by the columns of the part 1 is represented as R1 and the part column length of the columns of the part 2 is represented as R2, (R1+R2)×C is equal to the code length N (64,800 bits or 16,200 bits in the first embodiment) of the LDPC code to be subject to the block interleaving.

The part column length R1 is equal to a multiple of 360 bits which is the unit size P, and the part column length R2 is equal to the remainder when the sum (hereinafter, referred to as a column length) R1+R2 of the part column length R1 of the part 1 and the part column length R2 of the part 2 is divided by 360 bits which is the unit size P.

Here, the column length R1+R2 is equal to the value obtained by dividing the code length N of the LDPC code to be subject to the block interleaving by the number of bits m of the symbol.

When 16-QAM is adopted as the modulation scheme, since the number of bits m of the symbol is 4 bits, the column length R1+R2 of the LDPC code having a code length N of 16,200 bits is 4,050(=16,200/4) bits.

Furthermore, since the remainder when the column length R1+R2=4,050 is divided by 360 bits which is the unit size P is 90, the part column length R2 of the part 2 is 90 bits.

The part column length R1 of the part 1 is R1+R2−R2=4,050−90=3,960 bits.

FIG. 106 is a diagram showing the number of columns C of the parts 1 and 2 for combinations of the code lengths N and the modulation schemes and the part column lengths (the number of rows) R1 and R2.

FIG. 106 shows the number of columns C of the parts 1 and 2 for the combinations of the LDPC codes having the code lengths N of 16,200 bits and 64,800 bits and the modulation schemes of QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM and the part column lengths R1 and R2.

FIG. 107 is a diagram for describing the block interleaving performed in the block interleaver 25 of FIG. 105.

The block interleaver 25 performs the block interleaving by writing and reading the LDPC code in and from the parts 1 and 2.

That is, in the block interleaving, as shown in FIG. 107A, the writing of the code bits of the LDPC code of the one codeword in the columns of the part 1 from the top to the bottom (in column direction) is performed in the columns from the left to the right.

When the writing of the code bits in the bottommost region of the rightmost column (C-th column) of the columns of the part 1 is ended, the writing of the remaining code bits in the columns of the part 2 from the top to the bottom (in the column direction) is performed in the columns from the left to the right.

Subsequently, when the writing of the code bits in the bottommost region of the rightmost column (C-th column) of the columns of the part 2 is ended, the code bits are read from the first columns of all of C number of columns of the part 1 in the row direction for every C=m bits as shown in FIG. 107B.

The reading of the code bits from all of C number of columns of the part 1 is sequentially performed in the lower rows, and when the reading from the R1 row which is the last row is ended, the code bits are read from the first rows of all of C number of columns of the part 2 in the row direction for every C=m bits.

The reading of the code bits from all of C number of columns of the part 2 is sequentially performed in the lower rows, and the reading is performed up to the R2 row which is the last row.

As stated above, the code bits read for every m bits from the parts 1 and 2 are supplied as the symbol to the mapper 117 (FIG. 8).

Group-Wise Interleaving

FIG. 108 is a diagram for describing the group-wise interleaving performed in the group-wise interleaver 24 of FIG. 9.

In the group-wise interleaving, the LDPC code of one codeword is interleaved for every bit group according to a predetermined pattern (hereinafter, referred to as a GW pattern) by using 360 bits corresponding to one group obtained by dividing the LDPC code of one codeword from the leading code for every 360 bits equal to the unit size P into the bit groups.

Hereinafter, a (i+1)-th bit group from a leading bit group when the LDPC code of one codeword is divided into the bit groups is referred to as a bit group i.

When the unit size P is 360 bits, the LDPC code having the code length N of, for example, 1,800 bits is divided into 5 (=1,800/360) bit groups of bit groups 0, 1, 2, 3, and 4. For example, the LDPC code having the code length N of 16,200 bits is divided into 45 (=16,200/360) bit groups of bit groups 0, 1, . . . , and 44, and the LDPC code having the code length N of 64,800 bits is divided into 180 (=64,800/360) bit groups of bit groups 0, 1, . . . , and 179.

In the following description, it is assumed that the GW pattern is represented as the arrangement of numbers representing the bit groups. For example, the GW pattern of 4, 2, 0, 3, 1 for the LDPC code having the code length N of 1,800 bits represents that the arrangement of bit groups 0, 1, 2, 3, and 4 is interleaved (rearranged) into the arrangement of bit groups 4, 2, 0, 3, and 1.

The GW pattern can be set for at least the code length N of the LDPC code.

Example of GW Pattern for LDPC Code of 64 k Bits

FIG. 109 is a diagram showing a first example of the GW pattern for the LDPC code having a code length N of 64 k bits.

According to the GW pattern of FIG. 109, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into bit groups 39, 47, 96, 176, 33, 75, 165, 38, 27, 58, 90, 76, 17, 46, 10, 91, 133, 69, 171, 32, 117, 78, 13, 146, 101, 36, 0, 138, 25, 77, 122, 49, 14, 125, 140, 93, 130, 2, 104, 102, 128, 4, 111, 151, 84, 167, 35, 127, 156, 55, 82, 85, 66, 114, 8, 147, 115, 113, 5, 31, 100, 106, 48, 52, 67, 107, 18, 126, 112, 50, 9, 143, 28, 160, 71, 79, 43, 98, 86, 94, 64, 3, 166, 105, 103, 118, 63, 51, 139, 172, 141, 175, 56, 74, 95, 29, 45, 129, 120, 168, 92, 150, 7, 162, 153, 137, 108, 159, 157, 173, 23, 89, 132, 57, 37, 70, 134, 40, 21, 149, 80, 1, 121, 59, 110, 142, 152, 15, 154, 145, 12, 170, 54, 155, 99, 22, 123, 72, 177, 131, 116, 44, 158, 73, 11, 65, 164, 119, 174, 34, 83, 53, 24, 42, 60, 26, 161, 68, 178, 41, 148, 109, 87, 144, 135, 20, 62, 81, 169, 124, 6, 19, 30, 163, 61, 179, 136, 97, 16, and 88.

FIG. 110 is a diagram showing a second example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 110, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 6, 14, 1, 127, 161, 177, 75, 123, 62, 103, 17, 18, 167, 88, 27, 34, 8, 110, 7, 78, 94, 44, 45, 166, 149, 61, 163, 145, 155, 157, 82, 130, 70, 92, 151, 139, 160, 133, 26, 2, 79, 15, 95, 122, 126, 178, 101, 24, 138, 146, 179, 30, 86, 58, 11, 121, 159, 49, 84, 132, 117, 119, 50, 52, 4, 51, 48, 74, 114, 59, 40, 131, 33, 89, 66, 136, 72, 16, 134, 37, 164, 77, 99, 173, 20, 158, 156, 90, 41, 176, 81, 42, 60, 109, 22, 150, 105, 120, 12, 64, 56, 68, 111, 21, 148, 53, 169, 97, 108, 35, 140, 91, 115, 152, 36, 106, 154, 0, 25, 54, 63, 172, 80, 168, 142, 118, 162, 135, 73, 83, 153, 141, 9, 28, 55, 31, 112, 107, 85, 100, 175, 23, 57, 47, 38, 170, 137, 76, 147, 93, 19, 98, 124, 39, 87, 174, 144, 46, 10, 129, 69, 71, 125, 96, 116, 171, 128, 65, 102, 5, 43, 143, 104, 13, 67, 29, 3, 113, 32, and 165.

FIG. 111 is a diagram showing a third example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 111, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 103, 116, 158, 0, 27, 73, 140, 30, 148, 36, 153, 154, 10, 174, 122, 178, 6, 106, 162, 59, 142, 112, 7, 74, 11, 51, 49, 72, 31, 65, 156, 95, 171, 105, 173, 168, 1, 155, 125, 82, 86, 161, 57, 165, 54, 26, 121, 25, 157, 93, 22, 34, 33, 39, 19, 46, 150, 141, 12, 9, 79, 118, 24, 17, 85, 117, 67, 58, 129, 160, 89, 61, 146, 77, 130, 102, 101, 137, 94, 69, 14, 133, 60, 149, 136, 16, 108, 41, 90, 28, 144, 13, 175, 114, 2, 18, 63, 68, 21, 109, 53, 123, 75, 81, 143, 169, 42, 119, 138, 104, 4, 131, 145, 8, 5, 76, 15, 88, 177, 124, 45, 97, 64, 100, 37, 132, 38, 44, 107, 35, 43, 80, 50, 91, 152, 78, 166, 55, 115, 170, 159, 147, 167, 87, 83, 29, 96, 172, 48, 98, 62, 139, 70, 164, 84, 47, 151, 134, 126, 113, 179, 110, 111, 128, 32, 52, 66, 40, 135, 176, 99, 127, 163, 3, 120, 71, 56, 92, 23 and 20.

FIG. 112 is a diagram showing a fourth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 112, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 139, 106, 125, 81, 88, 104, 3, 66, 60, 65, 2, 95, 155, 24, 151, 5, 51, 53, 29, 75, 52, 85, 8, 22, 98, 93, 168, 15, 86, 126, 173, 100, 130, 176, 20, 10, 87, 92, 175, 36, 143, 110, 67, 146, 149, 127, 133, 42, 84, 64, 78, 1, 48, 159, 79, 138, 46, 112, 164, 31, 152, 57, 144, 69, 27, 136, 122, 170, 132, 171, 129, 115, 107, 134, 89, 157, 113, 119, 135, 45, 148, 83, 114, 71, 128, 161, 140, 26, 13, 59, 38, 35, 96, 28, 0, 80, 174, 137, 49, 16, 101, 74, 179, 91, 44, 55, 169, 131, 163, 123, 145, 162, 108, 178, 12, 77, 167, 21, 154, 82, 54, 90, 177, 17, 41, 39, 7, 102, 156, 62, 109, 14, 37, 23, 153, 6, 147, 50, 47, 63, 18, 70, 68, 124, 72, 33, 158, 32, 118, 99, 105, 94, 25, 121, 166, 120, 160, 141, 165, 111, 19, 150, 97, 76, 73, 142, 117, 4, 172, 58, 11, 30, 9, 103, 40, 61, 43, 34, 56, and 116.

FIG. 113 is a diagram showing a fifth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 113, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 72, 59, 65, 61, 80, 2, 66, 23, 69, 101, 19, 16, 53, 109, 74, 106, 113, 56, 97, 30, 164, 15, 25, 20, 117, 76, 50, 82, 178, 13, 169, 36, 107, 40, 122, 138, 42, 96, 27, 163, 46, 64, 124, 57, 87, 120, 168, 166, 39, 177, 22, 67, 134, 9, 102, 28, 148, 91, 83, 88, 167, 32, 99, 140, 60, 152, 1, 123, 29, 154, 26, 70, 149, 171, 12, 6, 55, 100, 62, 86, 114, 174, 132, 139, 7, 45, 103, 130, 31, 49, 151, 119, 79, 41, 118, 126, 3, 179, 110, 111, 51, 93, 145, 73, 133, 54, 104, 161, 37, 129, 63, 38, 95, 159, 89, 112, 115, 136, 33, 68, 17, 35, 137, 173, 143, 78, 77, 141, 150, 58, 158, 125, 156, 24, 105, 98, 43, 84, 92, 128, 165, 153, 108, 0, 121, 170, 131, 144, 47, 157, 11, 155, 176, 48, 135, 4, 116, 146, 127, 52, 162, 142, 8, 5, 34, 85, 90, 44, 172, 94, 160, 175, 75, 71, 18, 147, 10, 21, 14, and 81.

FIG. 114 is a diagram showing a sixth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 114, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 8, 27, 7, 70, 75, 84, 50, 131, 146, 99, 96, 141, 155, 157, 82, 57, 120, 38, 137, 13, 83, 23, 40, 9, 56, 171, 124, 172, 39, 142, 20, 128, 133, 2, 89, 153, 103, 112, 129, 151, 162, 106, 14, 62, 107, 110, 73, 71, 177, 154, 80, 176, 24, 91, 32, 173, 25, 16, 17, 159, 21, 92, 6, 67, 81, 37, 15, 136, 100, 64, 102, 163, 168, 18, 78, 76, 45, 140, 123, 118, 58, 122, 11, 19, 86, 98, 119, 111, 26, 138, 125, 74, 97, 63, 10, 152, 161, 175, 87, 52, 60, 22, 79, 104, 30, 158, 54, 145, 49, 34, 166, 109, 179, 174, 93, 41, 116, 48, 3, 29, 134, 167, 105, 132, 114, 169, 147, 144, 77, 61, 170, 90, 178, 0, 43, 149, 130, 117, 47, 44, 36, 115, 88, 101, 148, 69, 46, 94, 143, 164, 139, 126, 160, 156, 33, 113, 65, 121, 53, 42, 66, 165, 85, 127, 135, 5, 55, 150, 72, 35, 31, 51, 4, 1, 68, 12, 28, 95, 59, and 108.

FIG. 115 is a diagram showing a seventh example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 115, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

FIG. 116 is a diagram showing an eighth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 116, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 11, 5, 8, 18, 1, 25, 32, 31, 19, 21, 50, 102, 65, 85, 45, 86, 98, 104, 64, 78, 72, 53, 103, 79, 93, 41, 82, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 4, 12, 15, 3, 10, 20, 26, 34, 23, 33, 68, 63, 69, 92, 44, 90, 75, 56, 100, 47, 106, 42, 39, 97, 99, 89, 52, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 6, 16, 14, 7, 13, 36, 28, 29, 37, 73, 70, 54, 76, 91, 66, 80, 88, 51, 96, 81, 95, 38, 57, 105, 107, 59, 61, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 0, 9, 17, 2, 27, 30, 24, 22, 35, 77, 74, 46, 94, 62, 87, 83, 101, 49, 43, 84, 48, 60, 67, 71, 58, 40, 55, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, and 179.

FIG. 117 is a diagram showing a ninth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 117, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 9, 18, 15, 13, 35, 26, 28, 99, 40, 68, 85, 58, 63, 104, 50, 52, 94, 69, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 8, 16, 17, 24, 37, 23, 22, 103, 64, 43, 47, 56, 92, 59, 70, 42, 106, 60, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 4, 1, 10, 19, 30, 31, 89, 86, 77, 81, 51, 79, 83, 48, 45, 62, 67, 65, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 6, 2, 0, 25, 20, 34, 98, 105, 82, 96, 90, 107, 53, 74, 73, 93, 55, 102, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 14, 7, 3, 27, 21, 33, 44, 97, 38, 75, 72, 41, 84, 80, 100, 87, 76, 57, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 5, 11, 12, 32, 29, 36, 88, 71, 78, 95, 49, 54, 61, 66, 46, 39, 101, 91, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, and 179.

FIG. 118 is a diagram showing a tenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 118, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107, 31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129, 52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97, 33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17, 15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130, 56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45, 78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96, 32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

FIG. 119 is a diagram showing an eleventh example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 119, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, and 179.

FIG. 120 is a diagram showing a twelfth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 120, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72, 116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9, 5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55, 103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28, 104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125, 58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101, 94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135, 141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47, 80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148, 154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42, 114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161, 167, 173, and 179.

FIG. 121 is a diagram showing a thirteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 121, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

FIG. 122 is a diagram showing a fourteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 122, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, and 179.

FIG. 123 is a diagram showing a fifteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 123, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 8, 112, 92, 165, 12, 55, 5, 126, 87, 70, 69, 94, 103, 78, 137, 148, 9, 60, 13, 7, 178, 79, 43, 136, 34, 68, 118, 152, 49, 15, 99, 61, 66, 28, 109, 125, 33, 167, 81, 93, 97, 26, 35, 30, 153, 131, 122, 71, 107, 130, 76, 4, 95, 42, 58, 134, 0, 89, 75, 40, 129, 31, 80, 101, 52, 16, 142, 44, 138, 46, 116, 27, 82, 88, 143, 128, 72, 29, 83, 117, 172, 14, 51, 159, 48, 160, 100, 1, 102, 90, 22, 3, 114, 19, 108, 113, 39, 73, 111, 155, 106, 105, 91, 150, 54, 25, 135, 139, 147, 36, 56, 123, 6, 67, 104, 96, 157, 10, 62, 164, 86, 74, 133, 120, 174, 53, 140, 156, 171, 149, 127, 85, 59, 124, 84, 11, 21, 132, 41, 145, 158, 32, 17, 23, 50, 169, 170, 38, 18, 151, 24, 166, 175, 2, 47, 57, 98, 20, 177, 161, 154, 176, 163, 37, 110, 168, 141, 64, 65, 173, 162, 121, 45, 77, 115, 179, 63, 119, 146, and 144.

FIG. 124 is a diagram showing a sixteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 124, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 103, 138, 168, 82, 116, 45, 178, 28, 160, 2, 129, 148, 150, 23, 54, 106, 24, 78, 49, 87, 145, 179, 26, 112, 119, 12, 18, 174, 21, 48, 134, 137, 102, 147, 152, 72, 68, 3, 22, 169, 30, 64, 108, 142, 131, 13, 113, 115, 121, 37, 133, 136, 101, 59, 73, 161, 38, 164, 43, 167, 42, 144, 41, 85, 91, 58, 128, 154, 172, 57, 75, 17, 157, 19, 4, 86, 15, 25, 35, 9, 105, 123, 14, 34, 56, 111, 60, 90, 74, 149, 146, 62, 163, 31, 16, 141, 88, 6, 155, 130, 89, 107, 135, 79, 8, 10, 124, 171, 114, 162, 33, 66, 126, 71, 44, 158, 51, 84, 165, 173, 120, 7, 11, 170, 176, 1, 156, 96, 175, 153, 36, 47, 110, 63, 132, 29, 95, 143, 98, 70, 20, 122, 53, 100, 93, 140, 109, 139, 76, 151, 52, 61, 46, 125, 94, 50, 67, 81, 69, 65, 40, 127, 77, 32, 39, 27, 99, 97, 159, 166, 80, 117, 55, 92, 118, 0, 5, 83, 177, and 104.

FIG. 125 is a diagram showing a seventeenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 125, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 104, 120, 47, 136, 116, 109, 22, 20, 117, 61, 52, 108, 86, 99, 76, 90, 37, 58, 36, 138, 95, 130, 177, 93, 56, 33, 24, 82, 0, 67, 83, 46, 79, 70, 154, 18, 75, 43, 49, 63, 162, 16, 167, 80, 125, 1, 123, 107, 9, 45, 53, 15, 38, 23, 57, 141, 4, 178, 165, 113, 21, 105, 11, 124, 126, 77, 146, 29, 131, 27, 176, 40, 74, 91, 140, 64, 73, 44, 129, 157, 172, 51, 10, 128, 119, 163, 103, 28, 85, 156, 78, 6, 8, 173, 160, 106, 31, 54, 122, 25, 139, 68, 150, 164, 87, 135, 97, 166, 42, 169, 161, 137, 26, 39, 133, 5, 94, 69, 2, 30, 171, 149, 115, 96, 145, 101, 92, 143, 12, 88, 81, 71, 19, 147, 50, 152, 159, 155, 151, 174, 60, 32, 3, 142, 72, 14, 170, 112, 65, 89, 175, 158, 17, 114, 62, 144, 13, 98, 66, 59, 7, 118, 48, 153, 100, 134, 84, 111, 132, 127, 41, 168, 110, 102, 34, 121, 179, 148, 55, and 35.

FIG. 126 is a diagram showing an eighteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 126, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 37, 98, 160, 63, 18, 6, 94, 136, 8, 50, 0, 75, 65, 32, 107, 60, 108, 17, 21, 156, 157, 5, 73, 66, 38, 177, 162, 130, 171, 76, 57, 126, 103, 62, 120, 134, 154, 101, 143, 29, 13, 149, 16, 33, 55, 56, 159, 128, 23, 146, 153, 141, 169, 49, 46, 152, 89, 155, 111, 127, 48, 14, 93, 41, 7, 78, 135, 69, 123, 179, 36, 87, 27, 58, 88, 170, 125, 110, 15, 97, 178, 90, 121, 173, 30, 102, 10, 80, 104, 166, 64, 4, 147, 1, 52, 45, 148, 68, 158, 31, 140, 100, 85, 115, 151, 70, 39, 82, 122, 79, 12, 91, 133, 132, 22, 163, 47, 19, 119, 144, 35, 25, 42, 83, 92, 26, 72, 138, 54, 124, 24, 74, 118, 117, 168, 71, 109, 112, 106, 176, 175, 44, 145, 11, 9, 161, 96, 77, 174, 137, 34, 84, 2, 164, 129, 43, 150, 61, 53, 20, 165, 113, 142, 116, 95, 3, 28, 40, 81, 99, 139, 114, 59, 67, 172, 131, 105, 167, 51, and 86.

FIG. 127 is a diagram showing a nineteenth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 127, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 58, 70, 23, 32, 26, 63, 55, 48, 35, 41, 53, 20, 38, 51, 61, 65, 44, 29, 7, 2, 113, 68, 96, 104, 106, 89, 27, 0, 119, 21, 4, 49, 46, 100, 13, 36, 57, 98, 102, 9, 42, 39, 33, 62, 22, 95, 101, 15, 91, 25, 93, 132, 69, 87, 47, 59, 67, 124, 17, 11, 31, 43, 40, 37, 85, 50, 97, 140, 45, 92, 56, 30, 34, 60, 107, 24, 52, 94, 64, 5, 71, 90, 66, 103, 88, 86, 84, 19, 169, 159, 147, 126, 28, 130, 14, 162, 144, 166, 108, 153, 115, 135, 120, 122, 112, 139, 151, 156, 16, 172, 164, 123, 99, 54, 136, 81, 105, 128, 116, 150, 155, 76, 18, 142, 170, 175, 83, 146, 78, 109, 73, 131, 127, 82, 167, 77, 110, 79, 137, 152, 3, 173, 148, 72, 158, 117, 1, 6, 12, 8, 161, 74, 143, 133, 168, 171, 134, 163, 138, 121, 141, 160, 111, 10, 149, 80, 75, 165, 157, 174, 129, 145, 114, 125, 154, 118, 176, 177, 178, and 179.

FIG. 128 is a diagram showing a twentieth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 128, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 40, 159, 100, 14, 88, 75, 53, 24, 157, 84, 23, 77, 140, 145, 32, 28, 112, 39, 76, 50, 93, 27, 107, 25, 152, 101, 127, 5, 129, 71, 9, 21, 96, 73, 35, 106, 158, 49, 136, 30, 137, 115, 139, 48, 167, 85, 74, 72, 7, 110, 161, 41, 170, 147, 82, 128, 149, 33, 8, 120, 47, 68, 58, 67, 87, 155, 11, 18, 103, 151, 29, 36, 83, 135, 79, 150, 97, 54, 70, 138, 156, 31, 121, 34, 20, 130, 61, 57, 2, 166, 117, 15, 6, 165, 118, 98, 116, 131, 109, 62, 126, 175, 22, 111, 164, 16, 133, 102, 55, 105, 64, 177, 78, 37, 162, 124, 119, 19, 4, 69, 132, 65, 123, 160, 17, 52, 38, 1, 80, 90, 42, 81, 104, 13, 144, 51, 114, 3, 43, 146, 163, 59, 45, 89, 122, 169, 44, 94, 86, 99, 66, 171, 173, 0, 141, 148, 176, 26, 143, 178, 60, 153, 142, 91, 179, 12, 168, 113, 95, 174, 56, 134, 92, 46, 108, 125, 10, 172, 154, and 63.

FIG. 129 is a diagram showing a twenty-first example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 129, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 143, 57, 67, 26, 134, 112, 136, 103, 13, 94, 16, 116, 169, 95, 98, 6, 174, 173, 102, 15, 114, 39, 127, 78, 18, 123, 121, 4, 89, 115, 24, 108, 74, 63, 175, 82, 48, 20, 104, 92, 27, 3, 33, 106, 62, 148, 154, 25, 129, 69, 178, 156, 87, 83, 100, 122, 70, 93, 50, 140, 43, 125, 166, 41, 128, 85, 157, 49, 86, 66, 79, 130, 133, 171, 21, 165, 126, 51, 153, 38, 142, 109, 10, 65, 23, 91, 90, 73, 61, 42, 47, 131, 77, 9, 58, 96, 101, 37, 7, 159, 44, 2, 170, 160, 162, 0, 137, 31, 45, 110, 144, 88, 8, 11, 40, 81, 168, 135, 56, 151, 107, 105, 32, 120, 132, 1, 84, 161, 179, 72, 176, 71, 145, 139, 75, 141, 97, 17, 149, 124, 80, 60, 36, 52, 164, 53, 158, 113, 34, 76, 5, 111, 155, 138, 19, 35, 167, 172, 14, 147, 55, 152, 59, 64, 54, 117, 146, 118, 119, 150, 29, 163, 68, 99, 46, 177, 28, 22, 30, and 12.

FIG. 130 is a diagram showing a twenty-second example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 130, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 116, 47, 155, 89, 109, 137, 103, 60, 114, 14, 148, 100, 28, 132, 129, 105, 154, 7, 167, 140, 160, 30, 57, 32, 81, 3, 86, 45, 69, 147, 125, 52, 20, 22, 156, 168, 17, 5, 93, 53, 61, 149, 56, 62, 112, 48, 11, 21, 166, 73, 158, 104, 79, 128, 135, 126, 63, 26, 44, 97, 13, 151, 123, 41, 118, 35, 131, 8, 90, 58, 134, 6, 78, 130, 82, 106, 99, 178, 102, 29, 108, 120, 107, 139, 23, 85, 36, 172, 174, 138, 95, 145, 170, 122, 50, 19, 91, 67, 101, 92, 179, 27, 94, 66, 171, 39, 68, 9, 59, 146, 15, 31, 38, 49, 37, 64, 77, 152, 144, 72, 165, 163, 24, 1, 2, 111, 80, 124, 43, 136, 127, 153, 75, 42, 113, 18, 164, 133, 142, 98, 96, 4, 51, 150, 46, 121, 76, 10, 25, 176, 34, 110, 115, 143, 173, 169, 40, 65, 157, 175, 70, 33, 141, 71, 119, 16, 162, 177, 12, 84, 87, 117, 0, 88, 161, 55, 54, 83, 74, and 159.

FIG. 131 is a diagram showing a twenty-third example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 131, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 62, 17, 10, 25, 174, 13, 159, 14, 108, 0, 42, 57, 78, 67, 41, 132, 110, 87, 77, 27, 88, 56, 8, 161, 7, 164, 171, 44, 75, 176, 145, 165, 157, 34, 142, 98, 103, 52, 11, 82, 141, 116, 15, 158, 139, 120, 36, 61, 20, 112, 144, 53, 128, 24, 96, 122, 114, 104, 150, 50, 51, 80, 109, 33, 5, 95, 59, 16, 134, 105, 111, 21, 40, 146, 18, 133, 60, 23, 160, 106, 32, 79, 55, 6, 1, 154, 117, 19, 152, 167, 166, 30, 35, 100, 74, 131, 99, 156, 39, 76, 86, 43, 178, 155, 179, 177, 136, 175, 81, 64, 124, 153, 84, 163, 135, 115, 125, 47, 45, 143, 72, 48, 172, 97, 85, 107, 126, 91, 129, 137, 83, 118, 54, 2, 9, 58, 169, 73, 123, 4, 92, 168, 162, 94, 138, 119, 22, 31, 63, 89, 90, 69, 49, 173, 28, 127, 26, 29, 101, 170, 93, 140, 147, 149, 148, 66, 65, 121, 12, 71, 37, 70, 102, 46, 38, 68, 130, 3, 113, and 151.

FIG. 132 is a diagram showing a twenty-fourth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 132, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 168, 18, 46, 131, 88, 90, 11, 89, 111, 174, 172, 38, 78, 153, 9, 80, 53, 27, 44, 79, 35, 83, 171, 51, 37, 99, 95, 119, 117, 127, 112, 166, 28, 123, 33, 160, 29, 6, 135, 10, 66, 69, 74, 92, 15, 109, 106, 178, 65, 141, 0, 3, 154, 156, 164, 7, 45, 115, 122, 148, 110, 24, 121, 126, 23, 175, 21, 113, 58, 43, 26, 143, 56, 142, 39, 147, 30, 25, 101, 145, 136, 19, 4, 48, 158, 118, 133, 49, 20, 102, 14, 151, 5, 2, 72, 103, 75, 60, 84, 34, 157, 169, 31, 161, 81, 70, 85, 159, 132, 41, 152, 179, 98, 144, 36, 16, 87, 40, 91, 1, 130, 108, 139, 94, 97, 8, 104, 13, 150, 137, 47, 73, 62, 12, 50, 61, 105, 100, 86, 146, 165, 22, 17, 57, 167, 59, 96, 120, 155, 77, 162, 55, 68, 140, 134, 82, 76, 125, 32, 176, 138, 173, 177, 163, 107, 170, 71, 129, 63, 93, 42, 52, 116, 149, 54, 128, 124, 114, 67, and 64.

FIG. 133 is a diagram showing a twenty-fifth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 133, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 18, 150, 165, 42, 81, 48, 63, 45, 93, 152, 25, 16, 174, 29, 47, 83, 8, 60, 30, 66, 11, 113, 44, 148, 4, 155, 59, 33, 134, 99, 32, 176, 109, 72, 36, 111, 106, 73, 170, 126, 64, 88, 20, 17, 172, 154, 120, 121, 139, 77, 98, 43, 105, 133, 19, 41, 78, 15, 7, 145, 94, 136, 131, 163, 65, 31, 96, 79, 119, 143, 10, 95, 9, 146, 14, 118, 162, 37, 97, 49, 22, 51, 127, 6, 71, 132, 87, 21, 39, 38, 54, 115, 159, 161, 84, 108, 13, 102, 135, 103, 156, 67, 173, 76, 75, 164, 52, 142, 69, 130, 56, 153, 74, 166, 158, 124, 141, 58, 116, 85, 175, 169, 168, 147, 35, 62, 5, 123, 100, 90, 122, 101, 149, 112, 140, 86, 68, 89, 125, 27, 177, 160, 0, 80, 55, 151, 53, 2, 70, 167, 114, 129, 179, 138, 1, 92, 26, 50, 28, 110, 61, 82, 91, 117, 107, 178, 34, 157, 137, 128, 40, 24, 57, 3, 171, 46, 104, 12, 144, and 23.

FIG. 134 is a diagram showing a twenty-sixth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 134, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, and 35.

FIG. 135 is a diagram showing a twenty-seventh example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 135, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 50, 109, 128, 153, 12, 48, 17, 147, 55, 173, 172, 135, 121, 99, 162, 52, 40, 129, 168, 103, 87, 134, 105, 179, 10, 131, 151, 3, 26, 100, 15, 123, 88, 18, 91, 54, 160, 49, 1, 76, 80, 74, 31, 47, 58, 161, 9, 16, 34, 41, 21, 177, 11, 63, 6, 39, 165, 169, 125, 114, 57, 37, 67, 93, 96, 73, 106, 83, 166, 24, 51, 142, 65, 43, 64, 53, 72, 156, 81, 4, 155, 33, 163, 56, 150, 70, 167, 107, 112, 144, 149, 36, 32, 35, 59, 101, 29, 127, 138, 176, 90, 141, 92, 170, 102, 119, 25, 75, 14, 0, 68, 20, 97, 110, 28, 89, 118, 154, 126, 2, 22, 124, 85, 175, 78, 46, 152, 23, 86, 27, 79, 130, 66, 45, 113, 111, 62, 61, 7, 30, 133, 108, 171, 143, 60, 178, 5, 122, 44, 38, 148, 157, 84, 42, 139, 145, 8, 104, 115, 71, 137, 132, 146, 164, 98, 13, 117, 174, 158, 95, 116, 140, 94, 136, 120, 82, 69, 159, and 19.

FIG. 136 is a diagram showing a twenty-eighth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 136, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, and 159.

FIG. 137 is a diagram showing a twenty-ninth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 137, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175.

FIG. 138 is a diagram showing a thirtieth example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 138, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 71, 38, 98, 159, 1, 32, 28, 177, 125, 102, 83, 17, 121, 151, 66, 92, 140, 6, 165, 23, 75, 91, 87, 108, 163, 50, 77, 39, 110, 128, 73, 148, 14, 5, 68, 37, 53, 93, 149, 26, 166, 48, 79, 10, 122, 150, 103, 178, 119, 101, 61, 34, 8, 86, 36, 138, 146, 72, 179, 143, 147, 89, 4, 107, 33, 144, 141, 40, 100, 29, 118, 63, 46, 20, 153, 90, 152, 124, 7, 30, 31, 43, 78, 120, 85, 25, 52, 47, 64, 81, 175, 94, 115, 15, 112, 99, 13, 21, 42, 169, 76, 19, 168, 16, 27, 162, 167, 164, 97, 82, 44, 106, 12, 109, 132, 145, 161, 174, 95, 0, 105, 134, 173, 84, 9, 65, 88, 54, 67, 116, 154, 80, 22, 172, 60, 111, 133, 56, 170, 104, 131, 123, 24, 49, 113, 136, 55, 3, 157, 156, 35, 58, 45, 155, 70, 59, 57, 171, 176, 74, 117, 18, 127, 114, 11, 69, 158, 129, 139, 62, 135, 96, 142, 41, 130, 160, 2, 126, 51, and 137.

FIG. 139 is a diagram showing a thirty-first example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 139, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 66, 61, 150, 157, 63, 42, 78, 44, 23, 154, 133, 101, 82, 26, 84, 123, 89, 31, 45, 102, 36, 134, 83, 117, 170, 27, 73, 137, 25, 32, 62, 91, 4, 20, 144, 145, 21, 74, 113, 148, 24, 135, 5, 19, 2, 34, 43, 168, 14, 64, 142, 115, 87, 38, 147, 39, 51, 152, 56, 86, 122, 76, 57, 129, 172, 6, 126, 10, 97, 85, 164, 3, 80, 90, 79, 124, 138, 120, 17, 103, 99, 116, 46, 98, 162, 151, 143, 11, 175, 160, 96, 132, 81, 171, 94, 65, 118, 161, 125, 178, 95, 112, 88, 174, 13, 35, 1, 167, 0, 128, 12, 58, 29, 169, 67, 28, 119, 166, 60, 55, 54, 130, 92, 146, 177, 149, 111, 9, 173, 179, 176, 75, 77, 114, 48, 159, 8, 141, 107, 139, 52, 100, 136, 105, 127, 47, 18, 69, 109, 16, 121, 59, 163, 165, 108, 106, 70, 22, 93, 41, 33, 110, 53, 140, 153, 158, 50, 15, 37, 72, 156, 7, 131, 49, 71, 68, 104, 30, 40, and 155.

FIG. 140 is a diagram showing a thirty-second example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 140, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 75, 83, 11, 24, 86, 104, 156, 76, 37, 173, 127, 61, 43, 139, 106, 69, 49, 2, 128, 140, 68, 14, 100, 8, 36, 73, 148, 65, 16, 47, 177, 6, 132, 45, 5, 30, 13, 22, 29, 27, 101, 150, 23, 90, 41, 93, 89, 92, 135, 4, 71, 87, 44, 124, 26, 64, 1, 129, 157, 130, 107, 18, 91, 118, 3, 82, 144, 113, 121, 54, 84, 97, 122, 120, 7, 154, 56, 134, 57, 161, 33, 116, 28, 96, 72, 172, 12, 115, 38, 164, 32, 167, 145, 17, 88, 39, 151, 80, 0, 136, 169, 142, 74, 147, 126, 166, 163, 40, 110, 171, 50, 160, 131, 70, 175, 103, 125, 77, 162, 31, 85, 66, 67, 52, 108, 159, 133, 42, 153, 21, 51, 119, 123, 98, 35, 48, 111, 149, 25, 58, 60, 158, 102, 59, 117, 20, 141, 143, 46, 53, 155, 15, 165, 152, 112, 176, 105, 178, 99, 174, 168, 114, 179, 78, 10, 19, 62, 63, 170, 138, 34, 109, 9, 146, 95, 94, 55, 137, 81, and 79.

FIG. 141 is a diagram showing a thirty-third example of the GW pattern for the LDPC code having the code length N of 64 k bits.

According to the GW pattern of FIG. 141, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 98, 159, 59, 125, 163, 89, 26, 4, 102, 70, 92, 36, 37, 142, 176, 95, 71, 19, 87, 45, 81, 47, 65, 170, 103, 48, 67, 61, 64, 35, 76, 80, 140, 77, 10, 167, 178, 155, 120, 156, 151, 12, 58, 5, 83, 137, 41, 109, 2, 66, 133, 62, 135, 28, 93, 128, 86, 57, 153, 161, 110, 52, 147, 141, 31, 79, 32, 88, 160, 84, 150, 6, 100, 73, 126, 164, 17, 42, 101, 7, 55, 105, 91, 22, 130, 154, 1, 82, 14, 0, 9, 21, 50, 165, 72, 138, 175, 106, 108, 3, 169, 30, 157, 54, 18, 20, 44, 34, 134, 107, 56, 53, 15, 162, 38, 166, 24, 33, 60, 85, 145, 115, 43, 39, 40, 124, 149, 144, 132, 96, 11, 146, 90, 129, 119, 111, 171, 8, 152, 121, 173, 131, 49, 27, 118, 16, 148, 68, 177, 94, 179, 13, 114, 75, 51, 117, 25, 46, 136, 143, 139, 113, 127, 174, 74, 29, 122, 158, 69, 97, 78, 63, 99, 112, 104, 116, 172, 168, 23, and 123.

It is possible to apply the first to thirty-third examples of the GW pattern for the LDPC code having the code length N of 64 k bits described above to any combination of LDPC codes having a code length N of 64 k bits and an arbitrary code rate r and an arbitrary modulation scheme (constellation).

It is possible to further improve an error rate of each of the combinations by setting the GW pattern to be applied for each of the combinations of the code lengths N of the LDPC code and the code rates r of the LDPC code and the modulation schemes (constellations) in the group-wise interleaving.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 109 to specifically the combination of the ETRI code of (64 k, 5/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 110 to specifically the combination of the ETRI code of (64 k, 5/15) and 16-QAM of FIG. 90, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 111 to specifically the combination of the ETRI code of (64 k, 5/15) and 64-QAM of FIG. 91, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 112 to specifically the combination of the Sony code of (64 k, 7/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 113 to specifically the combination of the Sony code of (64 k, 7/15) and 16-QAM of FIG. 90, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 114 to specifically the combination of the Sony code of (64 k, 7/15) and 64-QAM of FIG. 91, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 115 to specifically the combination of the Sony code of (64 k, 9/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 116 to specifically the combination of the Sony code of (64 k, 9/15) and 16-QAM of FIG. 90, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 117 to specifically the combination of the Sony code of (64 k, 9/15) and 64-QAM of FIG. 91, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 118 to specifically the combination of the Sony code of (64 k, 11/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 119 to specifically the combination of the Sony code of (64 k, 11/15) and 16-QAM of FIG. 90, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 120 to specifically the combination of the Sony code of (64 k, 11/15) and 64-QAM of FIG. 91, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 121 to specifically the combination of the Sony code of (64 k, 13/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 122 to specifically the combination of the Sony code of (64 k, 13/15) and 16-QAM of FIG. 90, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 123 to specifically the combination of the Sony code of (64 k, 13/15) and 64-QAM of FIG. 91, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 124 to specifically the combination of the ETRI code of (64 k, 5/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 125 to specifically the combination of the ETRI code of (64 k, 7/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 126 to specifically the combination of the Sony code of (64 k, 7/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 127 to specifically the combination of the Sony code of (64 k, 9/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 128 to specifically the combination of the NERC code of (64 k, 9/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 129 to specifically the combination of the Sony code of (64 k, 11/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 130 to specifically the combination of the Sony code of (64 k, 13/15) and 256-QAM of FIGS. 92 and 93, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 131 to specifically the combination of the ETRI code of (64 k, 5/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 132 to specifically the combination of the ETRI code of (64 k, 7/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 133 to specifically the combination of the Sony code of (64 k, 7/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 134 to specifically the combination of the Sony code of (64 k, 9/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 135 to specifically the combination of the NERC code of (64 k, 9/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 136 to specifically the combination of the Sony code of (64 k, 11/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 137 to specifically the combination of the Sony code of (64 k, 13/15) and 1024-QAM of FIGS. 94 and 95, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 138 to specifically the combination of the Samsung code of (64 k, 6/15) and 4096-QAM of FIGS. 96 and 97, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 139 to specifically the combination of the ETRI code of (64 k, 7/15) and 4096-QAM of FIGS. 96 and 97, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 140 to specifically the combination of the Samsung code of (64 k, 8/15) and 4096-QAM of FIGS. 96 and 97, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 141 to specifically the combination of the Sony code of (64 k, 9/15) and 4096-QAM of FIGS. 96 and 97, for example.

Example of GW Pattern for LDPC Code of 16 k Bits

FIG. 142 is a diagram showing a first example of the GW pattern for the LDPC code having a code length N of 16 k bits.

According to the GW pattern of FIG. 142, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 21, 41, 15, 29, 0, 23, 16, 12, 38, 43, 2, 3, 4, 20, 31, 27, 5, 33, 28, 30, 36, 8, 40, 13, 6, 9, 18, 24, 7, 39, 10, 17, 37, 1, 19, 22, 25, 26, 14, 32, 34, 11, 35, 42, and 44.

FIG. 143 is a diagram showing a second example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 143, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 1, 3, 2, 8, 5, 23, 13, 12, 18, 19, 17, 20, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 0, 4, 6, 7, 21, 16, 10, 15, 9, 11, 22, 14, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

FIG. 144 is a diagram showing a third example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 144, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 1, 4, 5, 6, 24, 21, 18, 7, 17, 12, 8, 20, 23, 29, 28, 30, 32, 34, 36, 38, 40, 42, 0, 2, 3, 14, 22, 13, 10, 25, 9, 27, 19, 16, 15, 26, 11, 31, 33, 35, 37, 39, 41, 43, and 44.

FIG. 145 is a diagram showing a fourth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 145, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 0, 4, 7, 18, 9, 19, 27, 32, 10, 12, 24, 8, 35, 30, 17, 22, 20, 36, 38, 40, 42, 2, 5, 1, 6, 14, 15, 23, 16, 11, 21, 26, 13, 29, 33, 31, 28, 25, 34, 37, 39, 41, 43, and 44.

FIG. 146 is a diagram showing a fifth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 146, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 37, 0, 41, 19, 43, 8, 38, 3, 29, 13, 22, 6, 4, 2, 9, 26, 39, 15, 12, 10, 33, 17, 20, 16, 21, 44, 42, 27, 7, 11, 30, 34, 24, 1, 23, 35, 36, 25, 31, 18, 28, 32, 40, 5, and 14.

FIG. 147 is a diagram showing a sixth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 147, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 6, 28, 17, 4, 3, 38, 13, 41, 44, 43, 7, 40, 19, 2, 23, 16, 37, 15, 30, 20, 11, 8, 1, 27, 32, 34, 33, 39, 5, 9, 10, 18, 0, 31, 29, 26, 14, 21, 42, 22, 12, 24, 35, 25, and 36.

FIG. 148 is a diagram showing a seventh example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 148, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 27, 11, 20, 1, 7, 5, 29, 35, 9, 10, 34, 18, 25, 28, 6, 13, 17, 0, 23, 16, 41, 15, 19, 44, 24, 37, 4, 31, 8, 32, 14, 42, 12, 2, 40, 30, 36, 39, 43, 21, 3, 22, 26, 33, and 38.

FIG. 149 is a diagram showing an eighth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 149, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 6, 7, 27, 2, 23, 10, 30, 22, 28, 24, 20, 37, 21, 4, 14, 11, 42, 16, 9, 15, 26, 33, 40, 5, 8, 44, 34, 18, 0, 32, 29, 19, 41, 38, 17, 25, 43, 35, 36, 13, 39, 12, 1, and 31.

FIG. 150 is a diagram showing a ninth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 150, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 38, 7, 9, 13, 21, 39, 12, 10, 1, 43, 15, 30, 0, 14, 3, 42, 34, 40, 24, 28, 35, 8, 11, 23, 4, 20, 17, 41, 19, 5, 37, 22, 32, 18, 2, 26, 44, 25, 33, 36, 27, 16, 6, and 29.

FIG. 151 is a diagram showing a tenth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 151, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 36, 6, 2, 20, 43, 17, 33, 22, 23, 25, 13, 0, 10, 7, 21, 1, 19, 26, 8, 14, 31, 35, 16, 5, 29, 40, 11, 9, 4, 34, 15, 42, 32, 28, 18, 37, 30, 39, 24, 41, 3, 38, 27, 12, and 44.

FIG. 152 is a diagram showing an eleventh example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 152, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 14, 22, 18, 11, 28, 26, 2, 38, 10, 0, 5, 12, 24, 17, 29, 16, 39, 13, 23, 8, 25, 43, 34, 33, 27, 15, 7, 1, 9, 35, 40, 32, 30, 20, 36, 31, 21, 41, 44, 3, 42, 6, 19, 37, and 4.

FIG. 153 is a diagram showing a twelfth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 153, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 11, 14, 7, 31, 10, 2, 26, 0, 32, 29, 22, 33, 12, 20, 28, 27, 39, 37, 15, 4, 5, 8, 13, 38, 18, 23, 34, 24, 6, 1, 9, 16, 44, 21, 3, 36, 30, 40, 35, 43, 42, 25, 19, and 41.

FIG. 154 is a diagram showing a thirteenth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 154, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 1, 27, 17, 30, 11, 15, 9, 7, 5, 6, 32, 33, 2, 14, 3, 39, 18, 12, 29, 13, 41, 31, 4, 43, 35, 34, 40, 10, 19, 44, 8, 26, 21, 16, 28, 0, 23, 38, 25, 36, 22, 37, 42, 24, and 20.

FIG. 155 is a diagram showing a fourteenth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 155, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 41, 2, 12, 6, 33, 1, 13, 11, 26, 10, 39, 43, 36, 23, 42, 7, 44, 20, 8, 38, 18, 22, 24, 40, 4, 28, 29, 19, 14, 5, 9, 0, 30, 25, 35, 37, 27, 32, 31, 34, 21, 3, 15, 17, and 16.

FIG. 156 is a diagram showing a fifteenth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 156, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 2, 30, 12, 7, 25, 27, 3, 15, 14, 4, 26, 34, 31, 13, 22, 0, 39, 23, 24, 21, 6, 38, 5, 19, 42, 11, 32, 28, 40, 20, 18, 36, 9, 41, 10, 33, 37, 1, 16, 8, 43, 29, 35, and 44.

FIG. 157 is a diagram showing a sixteenth example of the GW pattern for the LDPC code having the code length N of 16 k bits.

According to the GW pattern of FIG. 157, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 28, 21, 10, 15, 8, 22, 26, 2, 14, 1, 27, 3, 39, 20, 34, 25, 12, 6, 7, 40, 30, 29, 38, 16, 43, 33, 4, 35, 9, 32, 5, 36, 0, 41, 37, 18, 17, 13, 24, 42, 31, 23, 19, 11, and 44.

It is possible to apply the first to sixteenth examples of the GW pattern for the LDPC code having the code length N of 16 k bits to any combination of LDPC codes having a code length N of 16 k bits and an arbitrary code rate r and an arbitrary modulation scheme (constellation).

As mentioned above, it is possible to further improve an error rate of each of the combinations by setting the GW pattern to be applied for each of the combinations of the code lengths N of the LDPC code and the code rates r of the LDPC code and the modulation schemes (constellations) in the group-wise interleaving.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 142 to specifically the combination of the LGE code of (16 k, 6/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 143 to specifically the combination of the Sony code of (16 k, 8/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 144 to specifically the combination of the Sony code of (16 k, 10/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 145 to specifically the combination of the Sony code of (16 k, 12/15) and QPSK of FIG. 89, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 146 to specifically the combination of the LGE code of (16 k, 6/15) and 16-QAM of FIG. 101, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 147 to specifically the combination of the Sony code of (16 k, 8/15) and 16-QAM of FIG. 101, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 148 to specifically the combination of the Sony code of (16 k, 10/15) and 16-QAM of FIG. 101, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 149 to specifically the combination of the Sony code of (16 k, 12/15) and 16-QAM of FIG. 101, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 150 to specifically the combination of the LGE code of (16 k, 6/15) and 64-QAM of FIG. 102, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 151 to specifically the combination of the Sony code of (16 k, 8/15) and 64-QAM of FIG. 102, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 152 to specifically the combination of the Sony code of (16 k, 10/15) and 64-QAM of FIG. 102, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 153 to specifically the combination of the Sony code of (16 k, 12/15) and 64-QAM of FIG. 102, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 154 to specifically the combination of the LGE code of (16 k, 6/15) and 256-QAM of FIGS. 103 and 104, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 155 to specifically the combination of the Sony code of (16 k, 8/15) and 256-QAM of FIGS. 103 and 104, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 156 to specifically the combination of the Sony code of (16 k, 10/15) and 256-QAM of FIGS. 103 and 104, for example.

It is possible to achieve a favorable error rate by applying the GW pattern of FIG. 157 to specifically the combination of the Sony code of (16 k, 12/15) and 256-QAM of FIGS. 103 and 104, for example.

Simulation Result

FIG. 158 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 109 is applied to the combination of the ETRI code of (64 k, 5/15) and QPSK of FIG. 89.

FIG. 159 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 110 is applied to the combination of the ETRI code of (64 k, 5/15) and 16-QAM of FIG. 90.

FIG. 160 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 111 is applied to the combination of the ETRI code of (64 k, 5/15) and 64-QAM of FIG. 91.

FIG. 161 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 112 is applied to the combination of the Sony code of (64 k, 7/15) and QPSK of FIG. 89.

FIG. 162 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 113 is applied to the combination of the Sony code of (64 k, 7/15) and 16-QAM of FIG. 90.

FIG. 163 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 114 is applied to the combination of the Sony code of (64 k, 7/15) and 64-QAM of FIG. 91.

FIG. 164 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 115 is applied to the combination of the Sony code of (64 k, 9/15) and QPSK of FIG. 89.

FIG. 165 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 116 is applied to the combination of the Sony code of (64 k, 9/15) and 16-QAM of FIG. 90.

FIG. 166 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 117 is applied to the combination of the Sony code of (64 k, 9/15) and 64-QAM of FIG. 91.

FIG. 167 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 118 is applied to the combination of the Sony code of (64 k, 11/15) and QPSK of FIG. 89.

FIG. 168 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 119 is applied to the combination of the Sony code of (64 k, 11/15) and 16-QAM of FIG. 90.

FIG. 169 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 120 is applied to the combination of the Sony code of (64 k, 11/15) and 64-QAM of FIG. 91.

FIG. 170 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 121 is applied to the combination of the Sony code of (64 k, 13/15) and QPSK of FIG. 89.

FIG. 171 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 122 is applied to the combination of the Sony code of (64 k, 13/15) and 16-QAM of FIG. 90.

FIG. 172 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 123 is applied to the combination of the Sony code of (64 k, 13/15) and 64-QAM of FIG. 91.

FIG. 173 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 124 is applied to the combination of the ETRI code of (64 k, 5/15) and 256-QAM of FIGS. 92 and 93.

FIG. 174 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 125 is applied to the combination of the ETRI code of (64 k, 7/15) and 256-QAM of FIGS. 92 and 93.

FIG. 175 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 126 is applied to the combination of the Sony code of (64 k, 7/15) and 256-QAM of FIGS. 92 and 93.

FIG. 176 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 127 is applied to the combination of the Sony code of (64 k, 9/15) and 256-QAM of FIGS. 92 and 93.

FIG. 177 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 128 is applied to the combination of the NERC code of (64 k, 9/15) and 256-QAM of FIGS. 92 and 93.

FIG. 178 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 129 is applied to the combination of the Sony code of (64 k, 11/15) and 256-QAM of FIGS. 92 and 93.

FIG. 179 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 130 is applied to the combination of the Sony code of (64 k, 13/15) and 256-QAM of FIGS. 92 and 93.

FIG. 180 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 131 is applied to the combination of the ETRI code of (64 k, 5/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 181 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 132 is applied to the combination of the ETRI code of (64 k, 7/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 182 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 133 is applied to the combination of the Sony code of (64 k, 7/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 183 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 134 is applied to the combination of the Sony code of (64 k, 9/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 184 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 135 is applied to the combination of the NERC code of (64 k, 9/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 185 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 136 is applied to the combination of the Sony code of (64 k, 11/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 186 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 137 is applied to the combination of the Sony code of (64 k, 13/15) and 1024-QAM of FIGS. 94 and 95.

FIG. 187 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 138 is applied to the combination of the Samsung code of (64 k, 6/15) and 4096-QAM of FIGS. 96 and 97.

FIG. 188 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 139 is applied to the combination of the ETRI code of (64 k, 7/15) and 4096-QAM of FIGS. 96 and 97.

FIG. 189 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 140 is applied to the combination of the Samsung code of (64 k, 8/15) and 4096-QAM of FIGS. 96 and 97.

FIG. 190 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 141 is applied to the combination of the Sony code of (64 k, 9/15) and 4096-QAM of FIGS. 96 and 97.

FIG. 191 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 142 is applied to the combination of the LGE code of (16 k, 6/15) and QPSK of FIG. 89.

FIG. 192 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 143 is applied to the combination of the Sony code of (16 k, 8/15) and QPSK of FIG. 89.

FIG. 193 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 144 is applied to the combination of the Sony code of (16 k, 10/15) and QPSK of FIG. 89.

FIG. 194 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 145 is applied to the combination of the Sony code of (16 k, 12/15) and QPSK of FIG. 89.

FIG. 195 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 146 is applied to the combination of the LGE code of (16 k, 6/15) and 16-QAM of FIG. 101.

FIG. 196 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 147 is applied to the combination of the Sony code of (16 k, 8/15) and 16-QAM of FIG. 101.

FIG. 197 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 148 is applied to the combination of the Sony code of (16 k, 10/15) and 16-QAM of FIG. 101.

FIG. 198 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 149 is applied to the combination of the Sony code of (16 k, 12/15) and 16-QAM of FIG. 101.

FIG. 199 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 150 is applied to the combination of the LGE code of (16 k, 6/15) and 64-QAM of FIG. 102.

FIG. 200 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 151 is applied to the combination of the Sony code of (16 k, 8/15) and 64-QAM of FIG. 102.

FIG. 201 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 152 is applied to the combination of the Sony code of (16 k, 10/15) and 64-QAM of FIG. 102.

FIG. 202 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 153 is applied to the combination of the Sony code of (16 k, 12/15) and 64-QAM of FIG. 102.

FIG. 203 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 154 is applied to the combination of the LGE code of (16 k, 6/15) and 256-QAM of FIGS. 103 and 104.

FIG. 204 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 155 is applied to the combination of the Sony code of (16 k, 8/15) and 256-QAM of FIGS. 103 and 104.

FIG. 205 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 156 is applied to the combination of the Sony code of (16 k, 10/15) and 256-QAM of FIGS. 103 and 104.

FIG. 206 is a diagram showing a BER/FER curve as a simulation result of a simulation that measures an error rate when the GW pattern of FIG. 157 is applied to the combination of the Sony code of (16 k, 12/15) and 256-QAM of FIGS. 103 and 104.

FIGS. 158 to 206 show BER/FER curves when an AWGN channel is used as the communication channel 13 (FIG. 7) (upper drawings) and when a Rayleigh (fading) channel is used as the communication channel (lower drawings).

In FIGS. 158 to 206, “wbil” represents BER/FER curves when the parity interleaving, the group-wise interleaving and the block interleaving are performed, and “w/obil” represents BER/FER curves when the parity interleaving, the group-wise interleaving and the block interleaving are not performed.

According to FIGS. 158 to 206, unlike in the case where the parity interleaving, the group-wise interleaving and the block-wise interleaving are not performed, it can be seen that it is possible to improve the BER/FER and it is possible to achieve the favorable error rate in the case where the parity interleaving, the group-wise interleaving and the block interleaving are performed.

In addition to the QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM constellations having the arrangements of signal points shown in FIGS. 83 to 104 described above, it is possible to apply the GW patterns of FIGS. 109 to 157 to a constellation in which the arrangements of signal points shown in FIGS. 83 to 104 are symmetrically moved with respect to the I axis or the Q axis, a constellation in which the arrangements of signal points are symmetrically moved with respect to the origin, and a constellation in which the arrangements of signal points are rotated at an arbitrary angle with the origin as its center, and it is possible to obtain the same effects when the arrangements of signal points shown in FIGS. 83 to 104 are applied to the QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM constellations.

In addition to the QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM constellations having the arrangements of signal points shown in FIGS. 83 to 104 described above, it is possible to apply the GW patterns of FIGS. 109 to 157 to a constellation in which most significant bits (MSBs) and least significant bits (LSBs) of the symbols corresponding the signal points are switched in the arrangements of signal points shown in FIGS. 83 to 104, and it is possible to obtain the same effects when the arrangements of signal points shown in FIGS. 83 to 104 are applied to the QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM constellations.

Configuration Example of Reception Apparatus 12

FIG. 207 is a block diagram showing a configuration example of the reception apparatus 12 of FIG. 7.

An OFDM operation unit 151 receives an OFDM signal from the transmission apparatus 11 (FIG. 7), and performs signal processing on the OFDM signal. Data obtained by performing the signal processing with the OFDM operation unit 151 is supplied to a frame management unit 152.

The frame management unit 152 performs processing (frame analysis) on a frame constituted by data supplied from the OFDM operation unit 151, and respectively supplies a signal of target data obtained as the result and a signal of control data to frequency deinterleavers 161 and 153.

The frequency deinterleaver 153 performs frequency deinterleaving on the data from the frame management unit 152 for every symbol, and supplies data obtained as the result to a demapper 154.

The demapper 154 performs quadrature demodulation by demapping (signal point arrangement decoding) data (data on the constellation) from the frequency deinterleaver 153 based on the arrangement (constellation) of signal points determined through the quadrature modulation performed by the transmission apparatus 11, and supplies data ((likelihood of) LDPC code) obtained as the result to an LDPC decoder 155.

The LDPC decoder 155 performs LDPC decoding on the LDPC code from the demapper 154, and supplies LDPC target data (here, a BCH code) obtained as the result to a BCH decoder 156.

The BCH decoder 156 performs BCH decoding on the LDPC target data from the LDPC decoder 155, and outputs control data (signaling) obtained as the result.

Meanwhile, the frequency deinterleaver 161 performs frequency deinterleaving on the data from the frame management unit 152 for every symbol, and supplies data obtained as the result to a SISO/MISO decoder 162.

The SISO/MISO decoder 162 performs space-time decoding on the data from the frequency deinterleaver 161, and supplies data obtained as the result to a time deinterleaver 163.

The time deinterleaver 163 performs time deinterleaving on the data from the SISO/MISO decoder 162 for every symbol, and supplies data obtained as the result to a demapper 164.

The demapper 164 performs quadrature demodulation by demapping (signal point arrangement decoding) the data (data on the constellation) from the time deinterleaver 163 based on the arrangement (constellation) of signal points determined through the quadrature modulation performed by the transmission apparatus 11, and supplies data obtained as the result to a bit deinterleaver 165.

The bit deinterleaver 165 performs bit deinterleaving on the data from the demapper 164, and supplies (likelihood of) an LDPC code which is data on which the bit interleaving has been performed to an LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding on the LDPC code from the bit deinterleaver 165, and supplies LDPC target data (here, a BCH code) obtained as the result to a BCH decoder 167.

The BCH decoder 167 performs BCH decoding on the LDPC target data from the LDPC decoder 155, and supplies data obtained as the result to a BB descrambler 168.

The BB descrambler 168 performs BB descrambling on the data from the BCH decoder 167, and supplies data obtained as the result to a null deletion unit 169.

The null deletion unit 169 deletes the Nulls inserted by the padder 112 of FIG. 8 from the data from the BB descrambler 168, and supplies data obtained as the result to a demultiplexer 170.

The demultiplexer 170 splits one or more streams (target data) multiplexed to the data from the null deletion unit 169, performs necessary processing on the split data items, and outputs the processed data items as an output stream.

The reception apparatus 12 may be configured without including some of the blocks shown in FIG. 207. That is, for example, when the transmission apparatus 11 (FIG. 8) is configured without including the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120 and the frequency interleaver 124, the reception apparatus 12 may be configured without including the time deinterleaver 163, the SISO/MISO decoder 162, the frequency deinterleaver 161 and the frequency deinterleaver 153 which are the blocks respectively corresponding to the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120 and the frequency interleaver 124 of the transmission apparatus 11.

Configuration Example of Bit Deinterleaver 165

FIG. 208 is a block diagram showing a configuration example of the bit deinterleaver 165 of FIG. 207.

The bit deinterleaver 165 includes a block deinterleaver 54, and a group-wise deinterleaver 55, and performs (bit) deinterleaving of symbol bits of a symbol which is the data from the demapper 164 (FIG. 207).

That is, the block deinterleaver 54 performs block deinterleaving (reverse processing of the block interleaving) corresponding to the block interleaving performed by the block interleaver 25 of FIG. 9 on the symbol bits of the symbol from the demapper 164 as a target, that is, block deinterleaving that returns the positions of (likelihood of) the code bits of the LDPC code rearranged by the block interleaving to the original positions, and supplies an LDPC code obtained as the result to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleaving (reverse processing of the group-wise interleaving) corresponding to the group-wise interleaving performed by the group-wise interleaver 24 of FIG. 9 on the LDPC code from the block deinterleaver 54 as a target, that is, group-wise deinterleaving which returns the arrangement to the original arrangement by rearranging the code bits of the LDPC code whose arrangement is changed for every bit group by, for example, the group-wise interleaving described in FIG. 108.

Here, when the parity interleaving, the group-wise interleaving and the block interleaving are performed on the LDPC code supplied to the bit deinterleaver 165 from the demapper 164, it is possible to perform all of parity deinterleaving (reverse processing of the parity interleaving, that is, parity deinterleaving that returns the arrangement of the code bits of the LDPC code whose arrangement is changed by the parity interleaving to the original arrangement) corresponding to the parity interleaving, block deinterleaving corresponding to the block interleaving, and group-wise deinterleaving corresponding to the group-wise interleaving in the bit deinterleaver 165.

In the bit deinterleaver 165 of FIG. 208, the block deinterleaver 54 that performs the block deinterleaving corresponding to the block interleaving, and the group-wise deinterleaver 55 that performs the group-wise deinterleaving corresponding to the group-wise interleaving are provided. However, the block that performs the parity deinterleaving corresponding to the parity interleaving is not provided, and thus, the parity deinterleaving is not performed.

Accordingly, the LDPC code on which the block deinterleaving and the group-wise deinterleaving have been performed and the parity deinterleaving has not been performed is supplied to the LDPC decoder 166 from (the group-wise deinterleaver 55 of) the bit deinterleaver 165.

The LDPC decoder 166 performs the LDPC decoding on the LDPC code from the bit deinterleaver 165 by using a transformation check matrix (or the transformation check matrix (FIG. 29) obtained by performing row permutation on the parity check matrix of the ETRI method (FIG. 27)) obtained by at least performing column permutation corresponding to the parity interleaving on the parity check matrix H of the DVB method used in the LDPC encoding performed by the LDPC encoder 115 of FIG. 8, and outputs data obtained as the result as a decoded result of the LDPC target data.

FIG. 209 is a flowchart for describing the process performed by the demapper 164, the bit deinterleaver 165 and the LDPC decoder 166 of FIG. 208.

In step S111, the demapper 164 performs quadrature demodulation by demapping the data (data on the constellation mapped to the signal point) from the time deinterleaver 163, and supplies data obtained as the result to the bit deinterleaver 165. The process then proceeds to step S112.

In step S112, the bit deinterleaver 165 performs the deinterleaving (bit deinterleaving) on the data from the demapper 164, and the process proceeds to step S113.

That is, in step S112, in the bit deinterleaver 165, the block deinterleaver 54 performs the block deinterleaving on the data (symbol) from the demapper 164 as a target, and supplies the code bits of the LDPC code obtained as the result to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs the group-wise interleaving on the LDPC code from the block deinterleaver 54 as a target, and supplies (the likelihood of) the LDPC code obtained as the result to the LDPC decoder 166.

In step S113, the LDPC decoder 166 performs the LDPC decoding on the LDPC code from the group-wise deinterleaver 55 by using the parity check matrix H used in the LDPC encoding performed by the LDPC encoder 115 of FIG. 8, that is, by using, for example, the transformation check matrix obtained from the parity check matrix H, and outputs data obtained as the result as a decoded result of the LDPC target data to the BCH decoder 167.

Similarly to the case of FIG. 9, for the sake of convenience in the description, even in FIG. 208, the block deinterleaver 54 that performs the block deinterleaving and the group-wise deinterleaver 55 that performs the group-wise deinterleaving are individually provided, but the block deinterleaver 54 and the group-wise deinterleaver 55 may be integrally configured.

LDPC Decoding

The LDPC decoding performed in the LDPC decoder 166 of FIG. 207 will be further described.

As described above, in the LDPC decoder 166 of FIG. 207, the LDPC decoding is performed on the LDPC code from the group-wise deinterleaver 55 on which the block deinterleaving and the group-wise deinterleaving have been performed and the parity deinterleaving has not been performed by using the transformation check matrix (or the transformation check matrix (FIG. 29) obtained by performing the row permutation on the parity check matrix of the ETRI method (FIG. 27)) obtained by at least performing the column permutation corresponding to the parity deinterleaving on the parity check matrix H of the DVB method used in the LDPC encoding performed by the LDPC encoder 115 of FIG. 8.

Here, it has been previously suggested to use the LDPC decoding capable of allowing an operation frequency to fall within a sufficiently realizable range while suppressing a circuit scale by performing the LDPC decoding using the transformation check matrix (for example, see U.S. Pat. No. 4,224,777).

The LDPC decoding using the transformation check matrix that has been previously suggested will be described with reference to FIGS. 210 to 213.

FIG. 210 is a diagram showing an example of a parity check matrix H of the LDPC code having a code length N of 90 and a code rate of 2/3.

In FIG. 210 (similarly in FIGS. 211 and 212 to be described below), 0 is represented as a period (.).

In the parity check matrix H of FIG. 210, the parity matrix has the dual diagonal structure.

FIG. 211 is a diagram showing a parity check matrix H′ obtained by performing row permutation of Expression (11) and column permutation of Expression (12) on the parity check matrix H of FIG. 210.

Row permutation: (6s+t+1)-th row→(5t+s+1)-th row   (11)

Column permutation: (6x+y+61)-th column→(5y+x+61)-th column  (12)

Here, in Expressions (11) and (12), s, t, x and y are respectively integers in a range of 0≦s<5, 0≦t<6, 0≦x<5, and 0≦t<6.

According to the row permutation of Expression (11), the 1^(st), 7^(th), 13^(th), 19^(th) and 25^(th) rows which have a remainder of 1 by being divided by 6 are respectively permuted to the 1^(st), 2^(nd), 3^(rd), 4^(th) and 5^(th) rows, and the 2^(nd), 8^(th), 14^(th), 20^(th) and 26^(th) rows which have a remainder of 2 by being divided by 6 are respectively permuted to the 6^(th), 7^(th), 8^(th), 9^(th) and 10^(th) rows.

According to the column permutation of Expression (12), the permutation is performed on the 61^(st) column and the subsequent columns (parity matrix) such that the 61^(st), 67^(th), 73^(rd), 79^(th) and 85^(th) columns which have a remainder of 1 by being divided by 6 are respectively permuted to the 61^(st), 62^(nd), 63^(rd), 64^(th) and 65^(th) columns, and 62^(nd), 68^(th), 74^(th), 80^(th) and 86^(th) columns which have a remainder 2 by being divided by 6 are respectively permuted to the 66^(th), 67^(th), 68^(th), 69^(th) and 70^(th) columns.

In this manner, the matrix obtained by performing the row and column permutations on the parity check matrix H of FIG. 210 is the parity check matrix H′ of FIG. 211.

Here, the arrangement of the code bits of the LDPC code are not influenced even when the row permutation of the parity check matrix H is performed.

The column permutation of Expression (12) corresponds to the parity interleaving when the information length K is 60, the unit size P is 5 and the divisor q(=M/P) of the parity length M (here, 30) is 6 in the parity interleaving that interleaves the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit.

Accordingly, the parity check matrix H′ of FIG. 211 is a transformation check matrix obtained by at least performing the column permutation for permuting the (K+qx+y+1)-th column of the parity check matrix (hereinafter, appropriately referred to as an original parity check matrix) H of FIG. 210 to the (K+Py+x+1)-th column.

When the LDPC code of the original parity check matrix H of FIG. 210 is multiplied by the LDPC code on which the same permutation as Expression (12) has been performed, a 0 vector is output to the transformation check matrix H′ of FIG. 211. That is, when a row vector obtained by performing the column permutation of Expression (12) on the row vector c as the LDPC code (one codeword) of the original parity check matrix H is expressed as c′, since Hc^(T) becomes the 0 vector in view of properties of the parity check matrix, H′c′^(T) also becomes the 0 vector.

As stated above, the transformation parity check matrix H′ of FIG. 211 is a parity check matrix of the LDPC code c′ obtained by performing the column permutation of Expression (12) on the LDPC code c of the original parity check matrix H.

Accordingly, the column permutation of Expression (12) is performed on the LDPC code c of the original parity check matrix H, and decoding (LDPC decoding) is performed on the LDPC code c′ after the column permutation by using the transformation check matrix H′ of FIG. 211. As the decoded result, since reverse permutation of the column permutation of Expression (12) is performed, it is possible to obtain the same decoded result as that in the decoding of the LDPC code of the original parity check matrix H using the parity check matrix H.

FIG. 212 is a diagram showing the transformation check matrix H′ of FIG. 211 with a predetermined space for every 5×5 matrix.

In FIG. 212, the transformation check matrix H′ is represented as a combination of a 5×5 (=p×p) unit matrix which is the unit size P, a unit (hereinafter, appropriately referred to as a quasi-unit matrix) in which one or more is of the unit matrix become 0s, a matrix (hereinafter, approximately referred to as a shift matrix) obtained by cyclic-shifting the unit matrix or the quasi-unit matrix, the sum (hereinafter, appropriately referred to as a sum matrix) of two or more matrices of the unit matrix, the quasi-unit matrix and the shift matrix, and a 5×5 0 matrix.

The transformation check matrix H′ of FIG. 212 may include the 5×5 unit matrix, the quasi-unit matrix, the shift matrix, the sum matrix, and the 0 matrix. Thus, hereinafter, these 5×5 matrices (the unit matrix, the quasi-unit matrix, the shift matrix, the sum matrix, and the 0 matrix) constituting the transformation check matrix H′ are appropriately referred to as constitutive matrices.

It is possible to use an architecture in which the check node calculation and the variable node calculation are simultaneously performed p times in the decoding of the LDPC code of the parity check matrix represented as P×P constitutive matrices.

FIG. 213 is a block diagram showing a configuration example of a decoding device that performs such decoding.

That is, FIG. 213 shows the configuration example of the decoding device that performs decoding on the LDPC code by using the transformation check matrix H′ of FIG. 212 obtained by at least performing the column permutation of Expression (12) on the original parity check matrix H of FIG. 210.

The decoding device of FIG. 213 includes an edge data storing memory 300 including six FIFOs 300 ₁ to 300 ₆, a selector 301 that selects the FIFOs 300 ₁ to 300 ₆, a check node calculating unit 302, two cyclic shift circuits 303 and 308, an edge data storing memory 304 including 18 FIFOs 304 ₁ to 304 ₁₈, a selector 305 that selects the FIFOs 304 ₁ to 304 ₁₈, a reception data memory 306 that stores reception data, a variable node calculating unit 307, a decoded word calculating unit 309, a reception data rearrangement unit 310, and a decoded data rearrangement unit 311.

A method of storing data in the edge data storing memories 300 and 304 will be initially described.

The edge data storing memory 300 includes the FIFOs 300 ₁ to 300 ₆ of which there are 6 which is a value obtained by dividing 30 which is the number of rows of the transformation check matrix H′ of FIG. 212 by 5 which is the number of rows (unit size P) of the constitutive matrices. The FIFO 300 _(y) (y=1, 2, . . . , and 6) includes storage regions of multiple stages, and messages corresponding to five edges of which the number thereof corresponds to the number of the rows and the number of columns (unit size P) can be simultaneously read from and written in the storage region of each stage. The number of the stages of the storage regions of the FIFO 300 _(y) is 9 which is the maximum number of the number of 1s (Hamming weight) of the transformation check matrix of FIG. 212 in the row direction.

Data (message v_(i) from the variable nodes) corresponding to the positions of 1s from the first row to the fifth row of the transformation check matrix H′ of FIG. 212 is stored in the FIFO 300 ₁ while the data and the respective rows fill in the transverse direction (0 is ignored). That is, when an element in the j-th row and the i-th column is represented as (j, i), data corresponding to the positions of 1s of the 5×5 unit matrix from (1, 1) to (5, 5) of the transformation check matrix H′ is stored in the storage region of the first stage of the FIFO 300 ₁. Data corresponding to the positions of 1s of the shift matrix (matrix obtained by cyclic-shifting the 5×5 unit matrix to the right by 3) from (1, 21) to (5, 25) of the transformation check matrix H′ is stored in the storage region of the second stage. Similarly, data are stored in the storage regions of the third and eighth stages so as to be associated with the transformation check matrix H′. Data corresponding to the positions of 1s of the shift matrix (matrix obtained by cyclic-shifting a matrix obtained by replacing 1s of the first row of the 5×5 unit matrix with 0s to the right by 1) from (1, 86) to (5, 90) of the transformation check matrix H′ is stored in the storage region of the ninth stage.

Data corresponding to the positions of 1s from the sixth row to the tenth row of the transformation check matrix H′ of FIG. 212 is stored in the FIFO 300 ₂. That is, data corresponding to the positions of 1s of the first shift matrix constituting the sum matrix (sum matrix which is the sum of the first shift matrix obtained by cyclic-shifting the 5×5 unit matrix to the right by 1 and the second shift matrix obtained by cyclic-shifting the 5×5 unit matrix to the right by 2) from (6, 1) to (10, 5) of the transformation check matrix H′ is stored in the storage region of the first stage of the FIFO 300 ₂. Further, data corresponding to the positions of 1s of the second shift matrix constituting the sum matrix from (6, 1) to (10, 5) of the transformation check matrix H′ is stored in the storage region of the second stage.

That is, in the case of the constitutive matrices having two or more weights, when the constitutive matrices are represented as the sum of multiple matrices of a P×P unit matrix having a weight of 1, a quasi-unit matrix in which one or more 1s of the elements of 1s of the unit matrix become 0s, and a shift matrix obtained by cyclic-shifting the unit matrix or the quasi-unit matrix, data (messages corresponding to the edges belonging to the unit matrix, the quasi-unit matrix or the shift matrix) corresponding to the positions of 1s of the unit matrix having the weight of 1, the quasi-unit matrix or the shift matrix is stored in the same address (the same FIFO of the FIFOs 300 ₁ to 300 ₆).

Hereinafter, data are stored in the storage regions of the third to ninth stages so as to be associated with the transformation check matrix H′.

Similarly, data are stored in the FIFOs 300 ₃ to 300 ₆ so as to be associated with the transformation check matrix H′.

The edge data storing memory 304 includes FIFOs 304 ₁ to 304 ₁₈ of which there are 18 which is a value obtained by dividing 90 which is the number of rows of the transformation check matrix H′ by 5 which is the number of columns (unit size P) of the constitutive matrices. The FIFO 304 _(x) (x=1, 2, . . . , and 18) includes storage regions of multiple stages, and messages corresponding to five edges of which the number thereof corresponds to the number of rows and the number of columns (unit size P) can be simultaneously read from and written in the storage regions of the multiple stages.

Data (messages u_(j) from the check nodes) corresponding to the positions of 1s from the first column to the fifth column of the transformation check matrix H′ of FIG. 212 are stored in the FIFO 304 ₁ while the data and the respective columns fill in the longitudinal direction (0 is ignored). That is, data corresponding to the positions of 1s of the 5×5 unit matrix from (1, 1) to (5, 5) of the transformation check matrix H′ is stored in the storage region of the first stage of the FIFO 304 ₁. Data corresponding to the positions of 1s of the first shift matrix constituting the sum matrix (sum matrix of the first shift matrix obtained by cyclic-shifting the 5×5 unit matrix to the right by 1 and the second shift matrix obtained by cyclic-shifting the 5×5 unit matrix to the right by 2) from (6, 1) to (10, 5) of the transformation check matrix H′ is stored in the storage region of the second stage. Furthermore, data corresponding to the positions of 1s of the second shift matrix constituting the sum matrix from (6, 1) to (10, 5) of the transformation check matrix H′ is stored in the storage region of the third stage.

That is, in the case of the constitutive matrices having two or more weights, when the constitutive matrices are represented as the sum of multiple matrices of a P×P unit matrix having a weight of 1, a quasi-unit matrix in which one or more 1s of the elements of 1s of the unit matrix become 0s, and a shift matrix obtained by cyclic-shifting the unit matrix or the quasi-unit matrix, data (messages corresponding to the edges belonging to the unit matrix, the quasi-unit matrix or the shift matrix) corresponding to the positions of 1s of the unit matrix having the weight of 1, the quasi-unit matrix or the shift matrix is stored in the same address (the same FIFO of the FIFOs 304 ₁ to 304 ₁₈).

Hereinafter, data are stored in the storage regions of the fourth and fifth stages so as to be associated with the transformation check matrix H′. The number of the stages of the storage regions of the FIFO 304 ₁ is 5 which is the maximum number of the number of 1s (Hamming weight) from the first column to the fifth column of the transformation check matrix H′ in the row direction.

Similarly, data are stored in the FIFOs 304 ₂ to 304 ₃ so as to be associated with the transformation check matrix H′, and the respective lengths thereof (the number of stages) are 5. Similarly, data are stored in the FIFOs 304 ₄ to 304 ₁₂ so as to be associated with the transformation check matrix H′, and the respective lengths thereof are 3. Similarly, data are stored in the FIFOs 304 ₁₃ to 304 ₁₈ so as to be associated with the transformation check matrix H′, and the respective lengths thereof are 2.

Next, the operation of the decoding device of FIG. 213 will be described.

The edge data storing memory 300 includes the 6 FIFOs 300 ₁ to 300 ₆, and the FIFO for storing data is selected from the FIFOs 300 ₁ to 300 ₆ based on information (matrix data) D312 indicating a row of the transformation check matrix H′ of FIG. 212 to which 5 messages D311 supplied from the cyclic shift circuit 308 at the previous stage belong, and the five messages D311 are sequentially stored in the selected FIFO all at once. When data is read, the edge data storing memory 300 sequentially reads the five messages D300 ₁ from the FIFO 300 ₁, and supplies the read messages to the selector 301 at the next stage. After the reading of the messages from the FIFO 300 ₁ is finished, the edge data storing memory 300 sequentially reads the messages from the FIFO 300 ₂ to 300 ₆, and supplies the read messages to the selector 301.

The selector 301 selects the five messages from the FIFO of the FIFOs 300 ₁ to 300 ₆ from which the data is currently being read in response to a selector signal D301, and supplies the selected messages as messages D302 to the check node calculating unit 302.

The check node calculating unit 302 includes five check node calculators 302 ₁ to 302 ₅, performs the check node calculation according to Expression (7) by using the messages D302 (D302 ₁ to D302 ₅) (messages v_(i) of Expression (7)) supplied through the selector 301, and supplies five messages D303 (D303 ₁ to D303 ₅) (messages u_(j) of Expression (7)) obtained as the result of the check node calculation to the cyclic shift circuit 303.

The cyclic shift circuit 303 performs cyclic-shifting of the five messages D303 ₁ to D303 ₅ obtained in the check node calculating unit 302 based on information (matrix data) D305 indicating the corresponding edge based on how many times the cyclic-shifting is performed on the unit matrix (or the quasi-unit matrix) as the original matrix in the transformation check matrix H′, and supplies the result as a message D304 to the edge data storing memory 304.

The edge data storing memory 304 includes the 18 FIFO 304 ₁ to 304 ₁₈, and the FIFO for storing data is selected from the FIFOs 304 ₁ to 304 ₁₈ based on information D305 indicating the row of the transformation check matrix H′ to which the 5 messages D304 supplied from the cyclic shift circuit 303 at the previous stage belong, and the five messages D304 are sequentially stored in the selected FIFO all at once. When data is read, the edge data storing memory 304 sequentially reads the five messages D306 ₁ from the FIFO 304 ₁, and supplies the read messages to the selector 305 at the next stage. After the reading of the data from the FIFO 304 ₁ is finished, the edge data storing memory 304 sequentially reads the messages from the FIFO 304 ₂ to 304 ₁₈, and supplies the read messages to the selector 305.

The selector 305 selects the five messages from the FIFO of the FIFOs 304 ₁ to 304 ₁₈ from which the data is currently being read in response to a selector signal D307, and supplies the selected messages as messages D308 to the variable node calculating unit 307 and the decoded word calculating unit 309.

Meanwhile, the reception data rearrangement unit 310 rearranges an LDPC code D313 corresponding to the parity check matrix H of FIG. 210 which is received through the communication channel 13 by the column permutation of Expression (12), and supplies the rearranged LDPC code as reception data D314 to the reception data memory 306. The reception data memory 306 calculates reception LLRs (log-likelihood ratios) from the reception data D314 supplied from the reception data rearrangement unit 310, and supplies the reception LLRs as reception values D309 to the variable node calculating unit 307 and the decoded word calculating unit 309 by 5 LLRs all at once.

The variable node calculating unit 307 includes the five variable node calculators 307 ₁ to 307 ₅, performs the variable node calculation according to Expression (1) by using the messages D308 (D308 ₁ to D308 ₅) (messages u_(j) of Expression (1)) supplied through the selector 305 and the five reception values D309 (reception values u_(0i) of Expression (1)) supplied from the reception data memory 306, and supplies messages D310 (D310 ₁ to D310 ₅) (messages v_(i) of Expression (1)) to the cyclic shift circuit 308.

The cyclic shift circuit 308 performs the cyclic-shifting the messages D310 ₁ to D310 ₅ calculated in the variable node calculating unit 307 based on information indicating the corresponding edge based on how many times the cyclic-shifting is performed on the unit matrix (or the quasi-unit matrix) as the original matrix in the transformation check matrix H′, and supplies the result as a message D311 to the edge data storing memory 300.

It is possible to perform one decoding process (variable node calculation and check node calculation) on the LDPC code by performing the aforementioned operation once. After the LDPC code is decoded by a predetermined number of times, the decoding device of FIG. 213 obtains a final decoded result and outputs the obtained result in the decoded word calculating unit 309 and the decoded data rearrangement unit 311.

That is, the decoded word calculating unit 309 includes five decoded word calculators 309 ₁ to 309 ₅, calculates the decoded result (decoded word) based on Expression (5) by using the five messages D308 (D308 ₁ to D308 ₅) (messages u_(j) of Expression (5)) output from the selector 305 and the five reception values D309 (reception values u_(0i) of Expression (5)) supplied from the reception data memory 306, as the final stage of the multiple decoding processes, and supplies decoded data D315 obtained as the result to the decoded data rearrangement unit 311.

The decoded data rearrangement unit 311 rearranges the decoded data D315 supplied from the decoded word calculating unit 309 by performing reverse permutation of the column permutation of Expression (12) on the decoded data, and outputs the rearranged data as a final decoded result D316.

As described above, by performing one or both of the row permutation and the column permutation on the parity check matrix (original parity check matrix) and transforming the parity check matrix to the parity check matrix (transformation check matrix) capable of being represented as the combination of the P×P unit matrix, the quasi-unit matrix in which one or more 1s of the elements of 1s of the unit matrix become 0s, the shift matrix obtained by cyclic-shifting the unit matrix or the quasi-unit matrix, the sum matrix which is the sum of multiple matrices of the unit matrix, the quasi-unit matrix and the shift matrix, and the P×P 0 matrix, that is, the combination of the constitutive matrices, it is possible to adopt the architecture in which the check node calculation and the variable node calculation are simultaneously performed P times which is less than the number of rows and the number of columns in the decoding of the LDPC code. When the architecture in which the node calculations (the check node calculation and the variable node calculation) are simultaneously performed P times which is less than the number of rows and the number of column of the parity check matrix is adopted, it is possible to allow the operation frequency to fall within the realizable range and to repeatedly perform the decoding multiple times unlike in the case where the node calculations are simultaneously performed by the number equal to the number of rows and the number of columns of the parity check matrix.

Similarly to the decoding device of FIG. 213, for example, the LDPC decoder 166 constituting the reception apparatus 12 of FIG. 207 is configured to perform the LDPC decoding by simultaneously performing the check node calculation and the variable node calculation P times.

That is, for the sake of convenience in the description, when the parity check matrix of the LDPC code output from the LDPC encoder 115 constituting the transmission apparatus 11 of FIG. 8 is, for example, the parity check matrix H which is shown in FIG. 210 and includes the parity matrix having the dual diagonal structure, in the parity interleaver 23 of the transmission apparatus 11, the parity interleaving that interleaves the (K+qx+y+1)-th code bit to the position of the (K+Py+x+1)-th code bit is performed while the information length K is 60, the unit size P is 5 and the divisor q (=M/P) of the parity length M is 6.

As mentioned above, since the parity interleaving corresponds to the column permutation of Expression (12), it is not necessary to perform the column permutation of Expression (12) in the LDPC decoder 166.

For this reason, in the reception apparatus 12 of FIG. 207, the LDPC code on which the parity interleaving has not been performed, that is, the LDPC code on which the column permutation of Expression (12) has been performed is supplied to the LDPC decoder 166 from the group-wise deinterleaver 55, and the same processing as that of the decoding device of FIG. 213 is performed in the LDPC decoder 166 except for the fact that the column permutation of Expression (12) is not performed.

That is, FIG. 214 is a diagram showing a configuration example of the LDPC decoder 166 of FIG. 207.

In FIG. 214, since the LDPC decoder 166 has the same configuration as that of the decoding device of FIG. 213 except for the fact that the reception data rearrangement unit 310 of FIG. 213 is not provided and performs the same processing as that of the decoding device of FIG. 213 except for the fact that the column permutation of Expression (12) is not performed, the description thereof will be omitted.

As stated above, since the LDPC decoder 166 can be configured without including the reception data rearrangement unit 310, it is possible to reduce the scale further than that of the decoding device of FIG. 213.

For the sake of convenience in the description, in FIGS. 210 to 214, the code length N of the LDPC code is 90, the information length K is 60, the unit size (the number of rows and the number of columns of the constitutive matrices) P is 5, and the divisor q (=M/P) of the parity length M is 6. However, the code length N, the information length K, the unit size P, and the divisor q (=M/P) are not limited to the aforementioned values.

That is, in the transmission apparatus 11 of FIG. 8, the LDPC encoder 115 outputs, for example, the LDPC code in which the code length N is 64,800 or 16,200, the information length K is N−Pq(=N−M), the unit size P is 360 and the divisor q is M/P. However, it is possible to apply the LDPC decoder 166 of FIG. 214 to the case where the LDPC decoding is performed by simultaneously performing the check node calculation and the variable node calculation on the LDPC code P times.

Moreover, after the LDPC code is decoded in the LDPC decoder 166, when the part of the parity bits of the decoded result is not necessary and only the information bits of the decoded result are output, it is possible to configure the LDPC decoder 166 without providing the decoded data rearrangement unit 311.

Configuration Example of Block Deinterleaver 54

FIG. 215 is a block diagram showing a configuration example of the block deinterleaver 54 of FIG. 208.

The block deinterleaver 54 has the same configuration as that of the block interleaver 25 described in FIG. 105.

Accordingly, the block deinterleaver 54 includes the storage region called the part 1, and the storage region called the part 2, and both of the parts 1 and 2 are configured in such a manner that columns as the storage regions that store one bit in the row direction and store the predetermined number of bits in the column direction are arranged in the row direction by the number C equal to the number of bits m of the symbol.

The block deinterleaver 54 performs block interleaving by writing and reading the LDPC code in and from the parts 1 and 2.

In the block deinterleaving, the writing of the LDPC code (which is the symbol) is performed in the reading order of the LDPC code by the block interleaver 25 of FIG. 105.

In addition, in the block deinterleaving, the reading of the LDPC code is performed in the writing order of the LDPC code by the block interleaver 25 of FIG. 105.

That is, in the block interleaving performed in the block interleaver 25 of FIG. 105, the LDPC code is written in the column direction and is read in the row direction with respect to the parts 1 and 2. However, in the block deinterleaving performed by the block deinterleaver 54 of FIG. 215, the LDPC code is written in the row direction and is read in the column direction with respect to the parts 1 and 2.

Another Configuration Example of Bit Deinterleaver 165

FIG. 216 is a block diagram showing another configuration example of the bit deinterleaver 165 of FIG. 207.

In the drawing, the parts corresponding to the parts of FIG. 208 will be assigned the same reference numerals, and the description thereof will be appropriately omitted in the following description.

That is, the bit deinterleaver 165 of FIG. 216 has the same configuration as that of FIG. 208 except for the fact that the parity deinterleaver 1011 is newly provided.

In FIG. 216, the bit deinterleaver 165 includes a block deinterleaver 54, a group-wise deinterleaver 55, and a parity deinterleaver 1011, and performs bit interleaving on the code bits of the LDPC code from the demapper 164.

That is, the block deinterleaver 54 performs the block deinterleaving (reverse processing of the block interleaving) corresponding to the block interleaving performed by the block interleaver 25 of the transmission apparatus 11, that is, the block deinterleaving that returns the positions of the code bits switched by the block interleaving to the original positions on the LDPC code from the demapper 164 as a target, and supplies the LDPC code obtained as the result to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs the group-wise deinterleaving corresponding to the group-wise interleaving as rearrangement processing performed by the group-wise interleaver 24 of the transmission apparatus 11 on the LDPC code from the block deinterleaver 54 as a target.

The LDPC code obtained as the result of the group-wise deinterleaving is supplied to the parity deinterleaver 1011 from the group-wise deinterleaver 55.

The parity deinterleaver 1011 performs parity deinterleaving (reverse processing of the parity interleaving) corresponding to the parity interleaving performed by the parity interleaver 23 of the transmission apparatus 11, that is, parity deinterleaving that returns the code bits of the LDPC code whose arrangement is changed by the parity interleaving to the original rearrangement on the code bits on which the group-wise deinterleaving in the group-wise deinterleaver 55 has been performed as a target.

The LDPC code obtained as the result of the parity deinterleaving is supplied to the LDPC decoder 166 from the parity deinterleaver 1011.

Accordingly, in the bit deinterleaver 165 of FIG. 216, the LDPC code on which the block deinterleaving, the group-wise deinterleaving and the parity deinterleaving have been performed, that is, the LDPC code obtained by the LDPC encoding according to the parity check matrix H is supplied to the LDPC decoder 166.

The LDPC decoder 166 performs the LDPC decoding on the LDPC code from the bit deinterleaver 165 by using the parity check matrix H used in the LDPC encoding performed by the LDPC encoder 115 of the transmission apparatus 11. That is, the LDPC decoder 166 performs the LDPC decoding on the LDPC code from the bit deinterleaver 165 by using the parity check matrix H (of the DVB method) used in the LDPC encoding performed by the LDPC encoder 115 of the transmission apparatus 11, using the transformation check matrix obtained by at least performing the column permutation corresponding to the parity interleaving on the parity check matrix H (in the ETRI method, parity check matrix (FIG. 28) obtained by performing the column permutation on the parity check matrix (FIG. 27) used in the LDPC encoding), or using the transformation check matrix (FIG. 29) obtained by performing the row permutation on the parity check matrix (FIG. 27) used in the LDPC encoding.

Here, in FIG. 216, since the LDPC code obtained by the LDPC encoding according to the parity check matrix H is supplied to the LDPC decoder 166 from (the parity deinterleaver 1011 of) the bit deinterleaver 165, when the LDPC decoding on the LDPC code is performed using the parity check matrix H (of the DVB method) used in the LDPC encoding performed by the LDPC encoder 115 of the transmission apparatus 11 (in the ETRI method, the parity check matrix (FIG. 28) obtained by performing the column permutation on the parity check matrix (FIG. 27) used in the LDPC encoding), the LDPC decoder 166 may be configured using a decoding device that performs the LDPC decoding using, for example, a full serial decoding scheme in which the calculation of the messages (check node messages and the variable node messages) is sequentially performed on the nodes bit by bit or a decoding device that performs the LDPC decoding using a full parallel decoding scheme in which the calculation of the messages is simultaneously performed on all of the nodes (in parallel).

When the LDPC decoding on the LDPC code is performed using the transformation check matrix obtained by at least performing the column permutation corresponding to the parity interleaving (in the ETRI method, the transformation check matrix (FIG. 29) obtained by performing the row permutation on the parity check matrix (FIG. 27) used in the LDPC encoding) on the parity check matrix H (of the DVB method) used in the LDPC encoding performed by the LDPC encoder 115 of the transmission apparatus 11 in the LDPC decoder 166, the LDPC decoder 166 may be configured as a decoding device of an architecture in which the check node calculation and the variable node calculation are simultaneously performed P (or divisors of P other than 1) times. Here, the decoding device may be a decoding device (FIG. 213) having the reception data rearrangement unit 310 that switches the code bits of the LDPC code by performing the same column permutation as the column permutation (parity interleaving) for obtaining the transformation check matrix on the LDPC code.

For the sake in convenience in the description, in FIG. 216, the block deinterleaver 54 that performs the block deinterleaving, the group-wise deinterleaver 55 that performs the group-wise deinterleaving, and the parity deinterleaver 1011 that performs the parity deinterleaving are individually configured. However, similarly to the parity interleaver 23, the group-wise interleaver 24 and the block interleaver 25 of the transmission apparatus 11, two or more of the block deinterleaver 54, the group-wise deinterleaver 55 and the parity deinterleaver 1011 may be integrally configured.

2. Second Embodiment

However, in ATSC 3.0, two types of methods including a type A and a type B are adopted as the block interleaving method performed in (the block interleaver of) the bit interleaver 116 of FIG. 8.

Here, the block interleaving of the type A is a method in which the writing of the LDPC code on which the group-wise interleaving has been performed in the column direction of columns as m number of storage regions that are arranged in the row direction is iteratively performed on m number of columns. The block interleaving of the type B is a method in which the writing of the LDPC code on which the group-wise interleaving has been performed for every bit group in the row direction of m number of columns is iteratively performed.

As stated above, since the two types of methods including the type A and the type B are adopted as the block interleaving method, in the transmission apparatus 11, when the block interleaving is performed by (the block interleaver) of the bit interleaver 116, the LDPC code is written in and read from the storage regions depending on the type A or the type B.

However, in the block interleaving of the type A and the block interleaving of the type B, since the writing method and a part of the reading method performed on the storage regions are different, it is necessary to provide two types of address generating circuits for generating a write address of the LDPC code and a read address of the LDPC code in (the block interleaver of) the bit interleaver 116.

Similarly, in the reception apparatus 12, even when the block deinterleaving is performed by (the block deinterleaver of) the bit deinterleaver 165, the reading method and a part of the writing method performed on the storage regions are different depending on the type. For this reason, it is necessary to provide two types of address generating circuits for generating a read address of the LDPC code and a write address of the LDPC code in (the block deinterleaver of) the bit deinterleaver 165.

As mentioned above, since it is necessary to provide two types of address generating circuits by adopting two types of method including the type A and the type B as the block interleaving method, it has been requested that the two types of methods including the type A and the type B efficiently coexist by realizing the block interleaving of the type A and the block interleaving of the type B by using a common address generating circuit.

Thus, as the second embodiment, a method of allowing a plurality of block interleaving methods (type A and type B) to efficiently coexist in the data transmission using the LDPC code will be described.

Configuration Example of Bit Interleaver 116

FIG. 217 is a block diagram showing a configuration example of the bit interleaver 116 of FIG. 8.

In the drawing, the parts corresponding to those in FIG. 9 will be assigned the same reference numerals, and the description thereof will be appropriately omitted in the following description.

That is, the bit interleaver 116 of FIG. 217 has the shame configuration as that in FIG. 9 except for the fact that a group-wise interleaver 1021 and a block interleaver 1022 are provided instead of the group-wise interleaver 24 and the block interleaver 25 of FIG. 9.

In FIG. 217, the bit interleaver 116 includes the parity interleaver 23, the group-wise interleaver 1021, and the block interleaver 1022, and performs bit interleaving on the code bits of the LDPC code from the LDPC encoder 115.

The group-wise interleaver 1021 performs group-wise interleaving on the LDPC code from the parity interleaver 23, and supplies the LDPC code on which the group-wise interleaving has been performed to the block interleaver 1022.

Here, when it is assumed that the block interleaving of the type B is performed, the group-wise interleaver 1021 rewrites the GW pattern for the block interleaving of the type B into the GW pattern for the block interleaving of the type A such that when the block interleaving of the type A is performed, the same block interleaving result as that when the block interleaving of the type B is performed is obtained.

Further, when it is assumed that the block interleaving of the type A is performed, the group-wise interleaver 1021 rewrites the GW pattern for the block interleaving of the type A into the GW pattern for the block interleaving of the type B such that when the block interleaving of the type B is performed, the same block interleaving result as that when the block interleaving of the type A is performed is obtained.

For example, the block interleaver 1022 symbolizes the LDPC code corresponding to one code to a m-bit symbol which is a unit of mapping by performing the block interleaving for demultiplexing the LDPC code from the group-wise interleaver 1021, and supplies the symbol to the mapper 117 (FIG. 8).

The block interleaver 1022 corresponds to the block interleaving of the type A or the type B, and can perform the block interleaving of the type A or the type B.

Block Interleaver 1022 Corresponding to Block Interleaving of Type A

Here, the block interleaving of the type A will be described. FIG. 218 is a block diagram showing a configuration example of the block interleaver 1022 (FIG. 217) corresponding to the block interleaving of the type A.

The block interleaver 1022 corresponding to the block interleaving of the type A includes a storage region called a part 1, and a storage region called to a part 2.

Both of the parts 1 and 2 are configured in such a manner that columns as storage regions which store one bit in the row (transverse) direction and store a predetermined number of bits in the column (longitudinal) direction are arranged in the row direction by the number C equal to the number of bits m of the symbol.

When a part column length of the part 1 which is the number of bits stored in the column direction by columns of the part 1 is represented as R1 and a part column length of columns of the part 2 is represented as R2, (R1+R2)×C is equal to the code length N (64,800 bits or 16,200 bits in the second embodiment) of the LDPC code to be subject to the interleaving.

Moreover, the part column length R1 is equal to a multiple of 360 bits which is the unit size P, and the part column length R2 is equal to a remainder obtained by dividing a column length R1+R2 which is the sum of the part column length R1 of the part 1 and the part column length R2 of the part 2 by 360 bits which is the unit size P.

Here, the column length R1+R2 is equal to a value obtained by dividing the code length N of the LDPC code to be subjected to the block interleaving by m which is the number of bits of the symbol.

For example, when the modulation scheme of 16-QAM is performed on the LDPC code having a length code N of 16,200 bits, since the number of bits m of the symbol is 4 bits, the column length R1+R2 is 4,050 (=16,200/4) bits.

Further, since the remainder obtained by dividing the column length R1+R2=4,050 by 360 bits which is the unit size P is 90, the part column length R2 of the part 2 is 90 bits.

The part column length R1 of the part 1 is R1+R2−R2=4,050−90=3,960 bits.

FIG. 219 is a diagram showing the number of columns C of the parts 1 and 2 for combinations of the code lengths N and the modulation schemes and the part column lengths (the number of rows) R1 and R2.

FIG. 219 shows the number of columns C of the parts 1 and 2 for the combinations of the LDPC codes having the code lengths N of 16,200 bits and 64,800 bits and the modulation schemes of QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM and the part column lengths R1 and R2.

FIG. 220 is a diagram for describing the block interleaving of the type A performed in the block interleaver 1022 (FIG. 217).

The block interleaver 1022 performs the block interleaving of the type A by writing and reading the LDPC code in and from the parts 1 and 2.

That is, as shown in FIG. 220A, in the block interleaving of the type A, the writing of the code bits of the LDPC code of one codeword from the top to the bottom (in the column direction) of the columns of the part 1 is performed in the columns from the left to the right.

When the writing of the code bits in the bottommost region of the rightmost column (C-th column) of the columns of the part 1 is ended, the writing of the remaining code bits in the columns of the part 2 from the top to the bottom (in the column direction) is performed in the columns from the left to the right.

Subsequently, when the writing of the code bits in the bottommost region of the rightmost column (C-th column) of the columns of the part 2 is ended, the code bits are read from the first rows of all of C number of columns of the part 1 in the row direction for every C=m bits, as shown in FIG. 220B.

The reading of the code bits from all of C number of columns of the part 1 is sequentially performed in the lower rows, and when the reading from the R1 row which is the last row is ended, the code bits are read from the first rows of all of C number of columns of the part 2 in the row direction for every C=m bits.

The reading of the code bits from all of C number of columns of the part 2 is sequentially performed in the lower rows, and the reading is performed up to the R2 row which is the last row.

In this manner, the code bits read from the parts 1 and 2 for every m bits are supplied as a symbol to the mapper 117 (FIG. 8).

Group-Wise Interleaving

FIG. 221 is a diagram for describing the group-wise interleaving performed in the group-wise interleaver 1021 of FIG. 217.

In the group-wise interleaving, the LDPC code of one codeword is interleaved for every bit group according to a predetermined pattern (hereinafter, referred to as a GW pattern) by using 360 bits corresponding to one group obtained by dividing the LDPC code of one codeword from the leading code for every 360 bits equal to the unit size P into the bit groups.

When the unit size P is 360 bits, the LDPC code having the code length N of, for example, 1,800 bits is divided into 5 (=1,800/360) bit groups of bit groups 0, 1, 2, 3, and 4. For example, the LDPC code having the code length N of 16,200 bits is divided into 45 (=16,200/360) bit groups of bit groups 0, 1, . . . , and 44, and the LDPC code having the code length N of 64,800 bits is divided into 180 (=64,800/360) bit groups of bit groups 0, 1, . . . , and 179.

Hereinafter, the (i+1)-th bit group from the leading bit group when the LDPC code of one codeword is divided into the bit groups is represented as a bit group i. In the following description, it is assumed that the GW pattern is represented as the arrangement of numbers representing the bit groups. For example, the GW pattern of 4, 2, 0, 3, 1 for the LDPC code having the code length N of 1,800 bits represents that the arrangement of bit groups 0, 1, 2, 3, and 4 is interleaved (rearranged) into the arrangement of bit groups 4, 2, 0, 3, and 1.

Specific Example of Block Interleaving of Type A

Next, the bit interleaving performed in the bit interleaver 116 including the block interleaver 1022 corresponding to the block interleaving of the type A will be described with reference to FIGS. 222 and 223.

FIG. 222 shows a case 1 where the number of bit groups is N_(g)=12 and the number of columns is N_(c)=4 as a specific example of the block interleaving of the type A. In FIG. 222, each bit group is divided for every 360 bits.

In the case 1 of the block interleaving of the type A, a column length N_(r1) of the part 1 is floor(N_(g)/N_(c))×360=12/4×360=3×360 bits. Since a column length N_(r2) of the part 2 is (N_(g)×360−N_(r1)×N_(c))/N_(c)=(12×360−3×360×4)/4=0 bits, only the storage region of the part 1 is used, and the storage region of the part 2 is not used. A floor function is a function obtained by rounding numbers after a decimal point.

In FIG. 222, a parity interleaver (PIL) output represents an output from the parity interleaver 23, that is, an input of the group-wise interleaver 1021, and a group-wise interleaver (GWI) output represents an output of the group-wise interleaver 1021. That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the arrangement of bit groups 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, and 6 according to the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6.

The block interleaver 1022 performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the top to the bottom (in the column direction) in the columns from the left to the right.

Thus, as shown in “block interleaver (BLI) write” of FIG. 222, the code bits of the bit groups 4, 7 and 9 are written in the first column (leftmost column), the code bits of the bit groups 2, 12 and 8 are written in the second column, the code bits of the bit groups 10, 1 and 5 are written in the third column, and the code bits of the bit groups 11, 3 and 6 are written in the fourth column (rightmost column).

Thereafter, the writing of the code bits in the bottommost region of the fourth column (rightmost column) of the columns of the part 1 is ended, as shown in “BLI read” of FIG. 222, the code bits are read from the first rows of all of four columns of the part 1 in the row direction for every C=m bits. The reading of the code bits from all of four columns of the part 1 is sequentially performed in the lower rows, and the reading is performed up to the last row.

In this manner, the code bits read from the part 1 for every m bits are supplied as a symbol to the mapper 117 (FIG. 8). In the mapper 117, the LDPC code from the bit interleaver 116 is mapped to a signal point of 16 (2⁴) signal points representing the symbol for every symbol.

FIG. 223 shows a case 2 where the number of bit groups is N_(g)=14 and the number of columns is N_(c)=4 as a specific example of the block interleaving of the type A. In FIG. 223, each bit group is divided for every 360 bits.

In the case 2 of the block interleaving of the type A, a column length N_(r1) of the part 1 is floor(N_(g)/N_(c))×360=14/4×360=3×360 bits. Since a column length N_(r2) of the part 2 is (N_(g)×360−N_(r1)×N_(c))/N_(c)=(14×360−3×360×4)/4=(2×360)/4=180 bits, the storage region of the part 2 is used in addition to the storage region of the part 1.

In FIG. 223, the PIL output and the GWI output represent the input and output of the group-wise interleaver 1021. That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, and 5 according to the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5.

The block interleaver 1022 performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the top to the bottom (in the column direction) in the columns from the left to the right. When the writing of the code bits in the bottommost region of the rightmost column of the columns of the part 1 is ended, the writing of the remaining code bits in the columns of the part 2 from the top to the bottom (in the column direction) is performed in the columns from the left to the right.

Thus, as shown in “BLI write” of FIG. 223, in the part 1, the code bits of the bit groups 4, 7, and 13 are written in the first column (leftmost column), the code bits of the bit groups 2, 12, and 8 are written in the second column, the code bits of the bit groups 10, 1, and 14 are written in the third column, and the code bits of the bit groups 11, 3, and 6 are written in the fourth column (rightmost column).

In the part 2, the coding bits of the bit group 9-1 are written in the first column (left most column), the coding bits of the bit group 9-2 are written in the second column, the coding bits of the bit group 5-1 are written in the third column, and the coding bits of the bit group 5-2 are written in the fourth column (rightmost column).

Here, the bit group 9-1 and the bit group 9-2 are respectively 180 bits, and the bit group 9 is formed by these bit groups. The bit group 5-1 and the bit group 5-2 are respectively 180 bits, and the bit group 5 is formed by these bit groups.

Subsequently, when the writing of the cod bits in the bottommost region of the fourth column (rightmost column) of the columns of the part 2 is ended, the code bits are read from the first rows of all of four columns of the part 1 in the row direction for every C=m bits as shown in “BLI read” of FIG. 223.

The writing of the code bits from all of four columns of the part 1 is sequentially performed in the lower rows, and when the reading from the last row is ended, the code bits are read from the first rows of all of four columns of the part 2 in the row direction for every C=m bits.

The reading of the code bits from all of four columns of the part 2 is sequentially performed in the lower rows, and is performed up to the last row.

In this manner, the code bits read from the parts 1 and 2 for every m bits are supplied as the symbol to the mapper 117 (FIG. 8). In the mapper 117, the LDPC code from the bit interleaver 116 is mapped to a signal point of 16 (2⁴) signal points representing the symbol for every symbol.

Block Interleaver 1022 Corresponding to Block Interleaving of Type B

Next, the block interleaving of the type B will be described. FIG. 224 is a block diagram showing a configuration example of the block interleaver 1022 (FIG. 217) corresponding to the block interleaving of the type B.

The block interleaver 1022 corresponding to the block interleaving of the type B includes a storage region called a part 1, and a storage region called a part 2.

The part 1 is configured in such a manner that columns as storage regions that store one bit in the row (transverse) direction and store a predetermined number of bits in the column (longitudinal) direction are arranged in the row direction by the number C equal to the number of bits m of the symbol. The part 2 is configured in such a manner that rows as storage regions that store one bit in the column (longitudinal) direction and store a predetermined number of bits are arranged in the row (transverse) direction in the row direction.

When a part column length which is the number of bits stored in the column direction by the columns of the part 1 is represented as R1 and a low length of the rows of the part 2 is represented as R2, R1×C+R2 is equal to the code length N (in the second embodiment, 64,800 bits or 16,200 bits) of the LDPC code to be subject to the block interleaving.

The part column length R1 is equal to a multiple of 360 bits which is the unit size P, and the row length R2 is equal to a value obtained by multiplying the remainder when the column length R1+R2/C which is the sum of the part column length R1 of the part 1 and a value obtained by dividing the row length R2 by C is divided by 360 bits which is the unit size P by C.

Here, the column length R1+R2/C is equal to a value obtained by dividing the code length N of the LDPC code to be subject to the block interleaving by the number of bits m of the symbol.

For example, when the 16-QAM modulation scheme is performed on the LDPC code having a code length N of 16,200 bits, since the number of bits m of the symbol is 4 bits, the column length R1+R2/C is 4,050 (=16,200/4) bits.

In addition, the remainder when the column length R1+R2/C=4,050 is divided by 360 bits which is the unit size P is 90, the row length R2 of the part 2 is 360(=90×4) bits.

The part column length R1 of the part 1 is R1+R2/C−R2/4=4,050−90=3,960 bits.

FIG. 225 is a diagram for describing the block interleaving of the type B performed in the block interleaver 1022 (FIG. 217).

The block interleaver 1022 performs the block interleaving of the type B by writing and reading the LDPC code in and from the parts 1 and 2.

That is, as shown in FIG. 225A, in the block interleaving of the type B, the writing of the code bits of the LDPC code of one codeword in the columns of the part 1 from the left to the right (in the row direction) for every bit group is iteratively performed.

When the writing of the code bits in the bottommost region of the rightmost column (C-th column) of the columns of the part 1 is ended, the writing of the remaining code bits is performed in the rows of the part 2 from the left to the right (in the row direction).

Thereafter, when the writing of the code bits in the rightmost row of the rows of the part 2 is ended, the code bits are read from the first rows of all of C number of columns of the part 1 in the row direction for every C=m bits, as shown in FIG. 225B.

The reading of the code bits from all of C number of columns of the part 1 is sequentially performed in the lower rows, and when the reading from the R1 row which is the last row is ended, the code bits are read from the rows of the part 2 from the left to the right (in the row direction) for every C=m bits.

In this manner, the code bits read from the parts 1 and 2 for every m bits are supplied as the symbol to the mapper 117 (FIG. 8).

Specific Example of Block Interleaving of Type B

Next, the bit interleaving performed in the bit interleaver 116 having the block interleaver 1022 corresponding to the block interleaving of the type B will be described with reference to FIGS. 226 and 227.

FIG. 226 shows a case 1 where the number of bit groups is N_(g)=12 and the number of columns is N_(c)=4 as a specific example of the block interleaving of the type B. In FIG. 226, each bit group is divided for every 360 bits.

In the case 1 of the block interleaving of the type B, a column length N_(r1) of the part 1 is floor(N_(g)/N_(c))×360=12/4×360=3×360 bits. Since a row length N_(r2) of the part 2 is N_(g)×360−N_(r1)×N_(c)=12×360−3×360×4=0 bits, only the storage region of the part 1 is used, and the storage region of the part 2 is not used.

In FIG. 226, a PIL output and a GWI output represent an input and an output of the group-wise interleaver 1021. That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the arrangement of bit groups 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, and 6 according to the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6.

The block interleaver 1022 iteratively performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the left to the right (in the row direction) for every bit group.

Thus, as shown in “BLI write” of FIG. 226, the code bits of the bit groups 4, 12, and 5 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 9, 10 and 3 are written in the third column, and the code bits of the bit groups 2, 1 and 6 are written in the fourth column (rightmost column).

Thereafter, when the writing of the code bits in the bottommost region of the fourth column (rightmost column) of the part 1 is ended, as shown in “BLI read” of FIG. 226, the code bits are read from the first rows of all of four columns of the part 1 in the row direction for every C=m bits. The reading of the code bits from all of four columns of the part 1 is sequentially performed in the lower rows, and is performed up to the last row.

In this manner, the code bits read from the part 1 for every m bits are supplied as the symbol to the mapper 117 (FIG. 8). In the mapper 117, the LDPC code from the bit interleaver 116 is mapped to a signal point of 16 (2⁴) signal points representing the symbol for every symbol.

FIG. 227 shows a case 2 where the number of bit groups is N_(g)=14 and the number of columns is N_(c)=4 as a specific example of the block interleaving of the type B. In FIG. 227, each bit group is divided for every 360 bits.

In the case 2 of the block interleaving of the type B, a column length N_(r1) of the part 1 is floor(N_(g)/N_(c))×360=14/4×360=3×360 bits. Since a row length N_(r2) of the part 2 is N_(g)×360−N_(r1)×N_(c)=14×360−3×360×4=2×360 bits, the storage region of the part 2 is used in addition to the storage region of the part 1.

In FIG. 227, a PIL output and a GWI output represent an input and an output of the group-wise interleaver 1021. That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, and 5 according to the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5.

The block interleaver 1022 iteratively performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the left to the right (in the row direction) for every bit group. When the writing of the code bits in the bottommost region of the rightmost column of the columns of the part 1 is ended, the writing of the remaining code bits is performed on the rows of the part 2 from the left to the right (in the row direction).

Thus, as shown in “BLI write” of FIG. 227, in the part 1, the code bits of the bit groups 4, 12, and 14 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 13, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column (rightmost column). The code bits of the bit groups 9 and 5 are written in the rows of the part 2.

Subsequently, when the writing of the code bits in the rightmost row of the part 2 is ended, the code bits are read from the first rows of all of four columns of the part 1 in the row direction for every C=m bits, as shown in “BLI read” of FIG. 227.

The reading of the code bits from all of four columns of the part 1 is sequentially performed in the lower rows, and when the reading in the last row is ended, the code bits are read from the rows of the part 2 from the left to the right (in the row direction) for every C=m bits. Here, the code bits of the bit groups 9 and 5 written in the rows of the part 2 are read by 4 bits in sequence from the leading bit.

In this manner, the code bits read from the parts 1 and 2 for every m bits are supplied as the symbol to the mapper 117 (FIG. 8). In the mapper 117, the LDPC code from the bit interleaver 116 is mapped to a signal point of 16 (2 ⁴) signal points representing the symbol for every symbol.

Rewriting of GW Pattern Depending on Type of Block Interleaving

The group-wise interleaver 1021 has to prepare the GW pattern for the block interleaving of the type A and the GW pattern for the block interleaving of the type B depending on the type of the block interleaving performed in the block interleaver 1022 provided at the latter stage.

In the block interleaving of the type A and the block interleaving of the type B, since the writing method and a part of the reading method performed on the storage regions are different, it is necessary to provide two types of address generating circuits for each type. For this reason, it has been requested that the block interleaving of the type A and the block interleaving of the type B are realized by using a common address generating circuit as described above.

Thus, in the group-wise interleaver 1021, it is possible to realize the common address generating circuit by converting the GW pattern for the block interleaving of the type B into the GW pattern for the block interleaving of the type A or the GW pattern for the block interleaving of the type A into the GW pattern for the block interleaving of the type B.

Here, the rewriting (converting) of the GW pattern performed in the group-wise interleaver 1021 will be described with reference to FIGS. 228 and 229.

FIG. 228 shows a case 1 where the number of bit groups is N_(g)=12 and the number of columns is N_(c)=4 as a specific conversion example of the GW pattern.

In FIG. 228, the block interleaver 1022 corresponding to the block interleaving of the type A is illustrated on the left side in the drawing, and the block interleaver 1022 corresponding to the block interleaving of the type B is illustrated on the right side in the drawing.

Similarly to FIGS. 222 and 226 described above, in FIG. 228, in the block interleaving, only the storage region of the part 1 is used, and the storage region of the part 2 is not used. Each bit group is divided for every 360 bits.

In FIG. 228, a PIL output and a GWI output represent an output and an input of the group-wise interleaver 1021. As shown on the left side in the drawing, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the number of bit groups 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, and 6, and outputs the interleaved arrangement to the block interleaver 1022 corresponding to the block interleaving of the type A.

That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the arrangement of bit groups 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, and 6 according to the GW pattern of 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, 6 for the block interleaving of the type A.

The block interleaver 1022 corresponding to the block interleaving of the type A performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the top to the bottom (in the column direction) in the columns from the left to the right.

Thus, as shown in “Type ABLI write” on the left side in the drawing, the code bits of the bit groups 4, 12, and 5 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 9, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column (rightmost column). When the writing of the code bits in the bottommost region of the fourth column of the columns of the part 1 is ended, the writing of the code bits is ended.

Meanwhile, as shown on the right side in the drawing, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the arrangement of bit groups 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, and 6, and outputs the interleaved arrangement to the block interleaver 1022 corresponding to the block interleaving of the type B.

That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 into the arrangement of bit groups 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, and 6 according to the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6 for the block interleaving of the type B.

The block interleaver 1022 corresponding to the block interleaving of the type B iteratively performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the left to the right (in the row direction) for every bit group.

Thus, as shown in “Type B BLI write” on the right side in the drawing, the code bits of the bit groups 4, 12, and 5 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 9, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column (rightmost column). When the writing of the code bits in the bottommost region of the fourth column of the columns of the part 1 is ended, the writing of the code bits is ended.

In this manner, the group-wise interleaver 1021 performs the interleaving according to the GW pattern depending on the type of the block interleaving, and thus, in the block interleaver 1022, the writing results of the code bits written in the columns of the part 1 are the same in the block interleaving of the type A and the block interleaving of the type B.

That is, in both of the block interleaving of the type A and the block interleaving of the type B, the code bits of the bit groups 4, 12, and 5 are written in the first column, the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 9, 10, and 3 are written in the third column, the code bits of the bit groups 2, 1, and 6 are written in the fourth column.

As stated above, if the writing results of the code bits written in the columns of the part 1 are the same, it is possible to use the write address generated in any one of the address generating circuit for the block interleaving of the type A and the address generating circuit for the block interleaving of the type B. That is, it is possible to realize the block interleaving of the type A and the block interleaving of the type B by using the common address generating circuit.

Thus, in the group-wise interleaver 1021 of FIG. 228, when it is assumed that the block interleaving of the type B is performed, the GW pattern is rewritten such that the block interleaving result (the writing result of the code bits written in the columns of the part 1) obtained when the block interleaving of the type A is performed is the same as the block interleaving result obtained when the block interleaving of the type B is performed.

For example, in the group-wise interleaver 1021 of FIG. 228, when it is assumed that the block interleaving of the type B is performed, a case 1-1 where the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6 is set as the GW pattern for the block interleaving of the type B is supposed.

In this case 1-1, when the block interleaving is performed in the block interleaver 1022, the group-wise interleaver 1021 rewrites the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6 for the block interleaving of the type B into the GW pattern of 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, 6 for the block interleaving of the type A. Thus, the block interleaving result of the type A performed by the group-wise interleaver 1021 is the same as the block interleaving result of the type B.

In the group-wise interleaver 1021 of FIG. 228, when it is assumed that the block interleaving of the type A is performed, the GW pattern is rewritten such that the block interleaving result (writing result of the code bits written in the columns of the part 1) obtained when the block interleaving of the type B is performed is the same as the block interleaving result obtained when the block interleaving of the type A is performed.

For example, in the group-wise interleaver 1021 of FIG. 228, when it is assumed that the block interleaving of the type A is performed, a case 1-2 where the GW pattern of 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, 6 is set as the GW pattern for the block interleaving of the type A is supposed.

In the case 1-2, when the block interleaving of the type B is performed in the block interleaver 1022, the group-wise interleaver 1021 rewrites the GW pattern of 4, 12, 5, 7, 8, 11, 9, 10, 3, 2, 1, 6 for the block interleaving of the type A into the GW pattern of 4, 7, 9, 2, 12, 8, 10, 1, 5, 11, 3, 6 for the block interleaving of the type B. Thus, the block interleaving result of the type B performed by the group-wise interleaver 1021 is the same as the block interleaving result of the type A.

As mentioned above, it is possible to achieve the common address generating circuit by converting the GW pattern for the block interleaving of the type B into the GW pattern for the block interleaving of the type A or the GW pattern for the block interleaving of the type A into the GW pattern for the block interleaving of the type B by the group-wise interleaver 1021.

Further, since the GW pattern is merely rewritten in the group-wise interleaver 1021 depending on the type of the block interleaving, performance degradation due to the converting of the GW pattern does not occur. For example, when it is assumed that the block interleaving of the type A is performed, since the completely same performance is obtained in the case where the block interleaving of the type A is performed according to the GW pattern for the block interleaving of the type A and the case where the block interleaving of the type B is performed according to the GW pattern for the block interleaving of the type B, the performance degradation due to the converting of the GW pattern does not occur.

Similarly to FIGS. 222 and 226 described above, in the block interleaver 1022 of FIG. 228, the code bits are read from the columns of the part 1. In this manner, the code bits read from the part 1 are supplied as the symbol to the mapper 117 (FIG. 8).

FIG. 229 shows a case 2 where the number of bit groups is N_(g)=14 and the number of columns is N_(c)=4 as a specific conversion example of the GW pattern.

Similarly to FIG. 228 described above, in FIG. 229, the block interleaver 1022 corresponding to the block interleaving of the type A is illustrated on the right side in the drawing, and the block interleaver 1022 corresponding to the block interleaving of the type B is illustrated on the right side in the drawing.

Similarly to FIGS. 223 and 227 described above, in FIG. 229, in the block interleaving, the storage region of the part 2 is used in addition to the storage region of the part 1. Each bit group is divided for every 360 bits.

In FIG. 229, a PIL output and a GWI output represent an input and an output of the group-wise interleaver 1021. As shown on the left side in the drawing, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, and 5, and outputs the interleaved arrangement to the block interleaver 1022 corresponding to the block interleaving of the type A.

That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, and 5 according to the GW pattern of 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, 5 for the block interleaving of the type A.

The block interleaver 1022 corresponding to the block interleaving of the type A performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the top to the bottom (in the column direction) in the columns from the left to the right. When the writing of the code bits in the bottommost region of the rightmost column of the columns of the part 1 is ended, the writing of the remaining code bits in the columns of the part 2 from the top to the bottom (in the column direction) is performed in the columns from the left to the right.

Thus, as shown in “Type A BLI write” on the left side in the drawing, the code bits of the bit groups 4, 12, and 14 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 13, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column (rightmost column).

In the part 2, the coding bits of the bit group 9-1 are written in the first column (leftmost column), the coding bits of the bit group 9-2 are written in the second column, the coding bits of the bit group 5-1 are written in the third column, and the coding bits of the bit group 5-2 are written in the fourth column (rightmost column).

Here, the bit group 9-1 and the bit group 9-2 are respectively 180 bits, and the bit group 9 is formed by these groups. Further, the bit group 5-1 and the bit group 5-2 are respectively 180 bits, and the bit group 5 is formed by these groups. When the writing of the code bits in the bottommost region of the fourth column of the columns of the part 2 is ended, the writing of the code bits is ended.

Meanwhile, as shown on the right side in the drawing, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, and 5, and outputs the interleaved arrangement to the block interleaver 1022 corresponding to the block interleaving of the type B.

That is, the group-wise interleaver 1021 interleaves the arrangement of bit groups 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 into the arrangement of bit groups 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, and 5 according to the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5 for the block interleaving of the type B.

The block interleaver 1022 corresponding to the block interleaving of the type B iteratively performs the writing of the output from the group-wise interleaver 1021 in the columns of the part 1 from the left to the right (in the row direction) for every bit group. When the writing of the code bits in the bottommost region of the rightmost column of the columns of the part 1 is ended, the writing of the remaining code bits in the rows of the part 2 from the left to the right (in the row direction) is performed.

Thus, as shown in “Type B BLI write” on the right side in the drawing, the code bits of the bit groups 4, 12, and 14 are written in the first column (leftmost column), the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 13, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column (rightmost column). The code bits of the bit groups 9, and 5 are written in the rows of the part 2. When the writing of the code bits in the rightmost row of the rows of the part 2 is ended, the writing of the code bits is ended.

In this manner, the group-wise interleaver 1021 performs the interleaving according to the GW pattern depending on the type of the block interleaving, and thus, the writing results of the code bits written in the columns of the part 1 are the same in the block interleaving of the type A and the block interleaving of the type B in the block interleaver 1022.

That is, in both of the block interleaving of the type A and the block interleaving of the type B, the code bits of the bit groups 4, 12, and 14 are written in the first column, the code bits of the bit groups 7, 8, and 11 are written in the second column, the code bits of the bit groups 13, 10, and 3 are written in the third column, and the code bits of the bit groups 2, 1, and 6 are written in the fourth column.

Similarly to FIG. 228 described above, if the writing results of the code bits written in the columns of the part 1 are the same, it is possible to realize the block interleaving of the type A and the block interleaving of the type B by using the common address generating circuit.

Thus, in the group-wise interleaver 1021 of FIG. 229, when it is assumed that the block interleaving of the type B is performed, the GW pattern is rewritten such that the block interleaving result (writing result of the code bits written in the columns of the part 1) obtained when the block interleaving of the type A is performed is the same as the block interleaving result obtained when the block interleaving of the type B is performed.

For example, in the group-wise interleaver 1021 of FIG. 229, when it is assumed that the block interleaving of the type B is performed, a case 2-1 where the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5 is set as the GW pattern for the block interleaving of the type B is supposed.

In the case 2-1, when the block interleaving of the type A is performed in the block interleaver 1022, the group-wise interleaver 1021 rewrites the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5 for the block interleaving of the type B into the GW pattern of 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, 5 for the block interleaving of the type A. Thus, the block interleaving result of the type A performed by the group-wise interleaver 1021 is the same as the block interleaving result of the type B.

In the group-wise interleaver 1021 of FIG. 229, when it is assumed that the block interleaving of the type A is performed, the GW pattern is rewritten such that the block interleaving result (writing result of the code bits written in the columns of the part 1) obtained when the block interleaving of the type B is performed is the same as the block interleaving result obtained when the block interleaving of the type A is performed.

For example, in the group-wise interleaver 1021 of FIG. 229, when it is assumed that the block interleaving of the type A is performed, a case 2-2 where the GW pattern of 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, 5 is set as the GW pattern for the block interleaving of the type A is supposed.

In this case 2-2, when the block interleaving of the type B is performed in the block interleaver 1022, the group-wise interleaver 1021 rewrites the GW pattern of 4, 12, 14, 7, 8, 11, 13, 10, 3, 2, 1, 6, 9, 5 for the block interleaving of the type A into the GW pattern of 4, 7, 13, 2, 12, 8, 10, 1, 14, 11, 3, 6, 9, 5 for the block interleaving of the type B. Thus, the block interleaving result of the type B performed by the group-wise interleaver 1021 is the same as the block interleaving result of the type A.

In this manner, it is possible to realize the common address generating circuit of the columns of the part 1 by converting the GW pattern for the block interleaving of the type B into the GW pattern for the block interleaving of the type A or the GW pattern for the block interleaving of the type A into the GW pattern for the block interleaving of the type B by the group-wise interleaver 1021.

Moreover, since the GW pattern is merely rewritten depending on the type of the block interleaving in the group-wise interleaver 1021, performance degradation due to the GW pattern does not occur. For example, when it is assumed that the block interleaving of the type B is performed, since the completely same performance is obtained in the case where the block interleaving of the type B is performed according to the GW pattern for the block interleaving of the type B and the case where the block interleaving of the type A is performed according to the GW pattern for the block interleaving of the rewritten type A, the performance degradation due to the converting of the GW pattern does not occur.

Here, since the write addresses of the code bits are different in the block interleaving of the type A and the block interleaving of the type B for (the storage region) of the part 2, it is necessary to provide the address generating circuit for each type.

Similarly to FIGS. 223 and 227 described above, in the block interleaver 1022 of FIG. 229, the code bits are read from (the storage regions of) the part 1 and the part 2. In this manner, the code bits read from (the storage regions of) the part 1 and the part 2 are supplied as the symbol to the mapper 117 (FIG. 8).

Example of GW Pattern Set to MODCOD (LDPC Code of 64 k Bits)

FIG. 230 shows an example of the GW pattern set to the MODCOD which is the combination of the LDPC code of 64 k bits and the modulation scheme.

In FIG. 230, a case where “A”s are described in MODCODs which are combinations of code rates (CR) of 12 types of LDPC codes and 6 types of modulation schemes (MODs) means that it is assumed that the block interleaving of the type A is performed, and the GW patterns for the block interleaving of the type A are set to the MODCODs. A case where “B”s are described in MODCODS means that it is assumed that the block interleaving of the type B is performed, and the GW patterns for the block interleaving of the type B are set to the MODCODs.

In FIG. 230, in the MODCOD in which the modulation scheme is QPSK (MOD 2) and the code rate r of the LDPC code of 64 k bits is 2/15, it is assumed that the block interleaving of the type A is performed. Similarly, in the MODCODs in which the modulation scheme is QPSK (MOD 2) and the code rates r of the LDPC code of 64 k bits are 3/15, 4/15, 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed.

In FIG. 230, in the MODCODs in which the modulation scheme is 16-QAM (MOD 4) and the code rates r of the LDPC code of 64 k bits are 2/15, 3/15, 4/15, 6/15, 7/15, 10/15, 11/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 16-QAM (MOD 4) and the code rates r of the LDPC code of 64 k bits are 5/15, 8/15, and 9/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 230, in the MODCODs in which the modulation scheme is 64-QAM (MOD 6) and the code rates r of the LDPC code of 64 k bits are 2/15, 3/15, 4/15, 5/15, 6/15, 8/15, 11/15, and 12/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 64-QAM (MOD 6) and the code rates r of the LDPC code of 64 k bits are 7/15, 9/15, 10/15, and 13/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 230, in the MODCODs in which the modulation scheme is 256-QAM (MOD 8) and the code rates r of the LDPC code of 64 k bits are 2/15, 3/15, 4/15, 9/15, and 12/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 256-QAM (MOD 8) and the code rates r of the LDPC code of 64 k bits are 5/15, 6/15, 7/15, 8/15, 10/15, 11/15, and 13/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 230, in the MODCODs in which the modulation scheme is 1024-QAM (MOD 10) and the code rates r of the LDPC code of 64 k bits are 2/15, 3/15, 4/15, 6/15, 8/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 1024-QAM (MOD 10) and the code rates r of the LDPC code of 64 k bits are 5/15, 7/15, 9/15, 10/15, and 11/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 230, in the MODCODs in which the modulation scheme is 4096-QAM (MOD 12) and the code rates r of the LDPC code of 64 k bits are 2/15, 3/15, 4/15, 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed.

As stated above, the GW pattern for the block interleaving of the type A or the GW pattern for the block interleaving of the type B are set for each MODCOD which is the combination of the LDPC code of 64 k bits and the modulation scheme depending on the assumed type.

As described above, in the group-wise interleaver 1021, when it is assumed that the block interleaving of the type B is performed, the GW pattern for the block interleaving of the type B is rewritten into the GW pattern for the block interleaving of the type A such that the block interleaving result obtained when the block interleaving of the type A is performed is the same as the block interleaving result obtained when the block interleaving of the type B is performed.

Further, in the group-wise interleaver 1021, when it is assumed that the block interleaving of the type A is performed, the GW pattern for the block interleaving of the type A is rewritten into the GW pattern for the block interleaving of the type B such that the block interleaving result obtained when the block interleaving of the type B is performed is the same as the block interleaving result obtained when the block interleaving of the type A is performed.

Hereinafter, as a specific example of the GW pattern set to each MODCOD shown in FIG. 230, the GW pattern (hereinafter, referred to as an original GW pattern) for the block interleaving of the assumed type and the GW pattern rewritten (hereinafter, referred to as a converted pattern) in order to perform the block interleaving of the type different from the assumed type will be described. It is possible to apply the uniform constellation (UC) or the non-uniform constellation (NUC) to the QAM constellation such as 16-QAM.

In each MODCOD, when the GW pattern for the block interleaving of the type A is set as the original GW pattern (A), the GW pattern for the block interleaving of the type B is set as the converted GW pattern (B). By contrast, when the GW pattern for the block interleaving of the type B is set as the original GW pattern (B), the GW pattern for the block interleaving of the type A is set as the converted GW pattern (A).

FIG. 231 is a diagram showing an example of the GW pattern for the LDPC code having a code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 231, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 70, 149, 136, 153, 104, 110, 134, 61, 129, 126, 58, 150, 177, 168, 78, 71, 120, 60, 155, 175, 9, 161, 103, 123, 91, 173, 57, 106, 143, 151, 89, 86, 35, 77, 133, 31, 7, 23, 51, 5, 121, 83, 64, 176, 119, 98, 49, 130, 128, 79, 162, 32, 172, 87, 131, 45, 114, 93, 96, 39, 68, 105, 85, 109, 13, 33, 145, 18, 12, 54, 111, 14, 156, 8, 16, 73, 2, 84, 47, 42, 101, 63, 88, 25, 52, 170, 24, 69, 142, 178, 20, 65, 97, 66, 80, 11, 59, 19, 115, 154, 26, 147, 28, 50, 160, 102, 55, 139, 125, 116, 138, 167, 53, 169, 165, 99, 159, 148, 179, 0, 146, 90, 6, 100, 74, 117, 48, 75, 135, 41, 137, 76, 92, 164, 113, 152, 72, 36, 3, 163, 15, 46, 21, 44, 108, 34, 56, 140, 127, 158, 94, 67, 122, 1, 27, 171, 30, 157, 112, 81, 118, 43, 29, 124, 22, 62, 37, 40, 4, 107, 166, 82, 95, 10, 144, 141, 132, 174, 38, and 17.

According to the converted GW pattern (B) of FIG. 231, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 70, 20, 149, 65, 136, 97, 153, 66, 104, 80, 110, 11, 134, 59, 61, 19, 129, 115, 126, 154, 58, 26, 150, 147, 177, 28, 168, 50, 78, 160, 71, 102, 120, 55, 60, 139, 155, 125, 175, 116, 9, 138, 161, 167, 103, 53, 123, 169, 91, 165, 173, 99, 57, 159, 106, 148, 143, 179, 151, 0, 89, 146, 86, 90, 35, 6, 77, 100, 133, 74, 31, 117, 7, 48, 23, 75, 51, 135, 5, 41, 121, 137, 83, 76, 64, 92, 176, 164, 119, 113, 98, 152, 49, 72, 130, 36, 128, 3, 79, 163, 162, 15, 32, 46, 172, 21, 87, 44, 131, 108, 45, 34, 114, 56, 93, 140, 96, 127, 39, 158, 68, 94, 105, 67, 85, 122, 109, 1, 13, 27, 33, 171, 145, 30, 18, 157, 12, 112, 54, 81, 111, 118, 14, 43, 156, 29, 8, 124, 16, 22, 73, 62, 2, 37, 84, 40, 47, 4, 42, 107, 101, 166, 63, 82, 88, 95, 25, 10, 52, 144, 170, 141, 24, 132, 69, 174, 142, 38, 178, and 17.

FIG. 232 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 232, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 75, 170, 132, 174, 7, 111, 30, 4, 49, 133, 50, 160, 92, 106, 27, 126, 116, 178, 41, 166, 88, 84, 80, 153, 103, 51, 58, 107, 167, 39, 108, 24, 145, 96, 74, 65, 8, 40, 76, 140, 44, 68, 125, 119, 82, 53, 152, 102, 38, 28, 86, 162, 171, 61, 93, 147, 117, 32, 150, 26, 59, 3, 148, 173, 141, 130, 154, 97, 33, 172, 115, 118, 127, 6, 16, 0, 143, 9, 100, 67, 98, 110, 2, 169, 47, 83, 164, 155, 123, 159, 42, 105, 12, 158, 81, 20, 66, 57, 121, 25, 1, 90, 175, 35, 60, 79, 87, 135, 10, 139, 156, 177, 77, 89, 73, 113, 52, 109, 134, 36, 176, 54, 69, 146, 31, 15, 71, 18, 95, 124, 85, 14, 78, 129, 161, 19, 72, 13, 122, 21, 63, 137, 120, 144, 91, 157, 48, 34, 46, 22, 29, 104, 45, 56, 151, 62, 43, 94, 163, 99, 64, 138, 101, 23, 11, 17, 136, 128, 114, 112, 165, 5, 142, 179, 37, 70, 131, 55, 168, and 149.

According to the converted GW pattern (B) of FIG. 232, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 75, 42, 170, 105, 132, 12, 174, 158, 7, 81, 111, 20, 30, 66, 4, 57, 49, 121, 133, 25, 50, 1, 160, 90, 92, 175, 106, 35, 27, 60, 126, 79, 116, 87, 178, 135, 41, 10, 166, 139, 88, 156, 84, 177, 80, 77, 153, 89, 103, 73, 51, 113, 58, 52, 107, 109, 167, 134, 39, 36, 108, 176, 24, 54, 145, 69, 96, 146, 74, 31, 65, 15, 8, 71, 40, 18, 76, 95, 140, 124, 44, 85, 68, 14, 125, 78, 119, 129, 82, 161, 53, 19, 152, 72, 102, 13, 38, 122, 28, 21, 86, 63, 162, 137, 171, 120, 61, 144, 93, 91, 147, 157, 117, 48, 32, 34, 150, 46, 26, 22, 59, 29, 3, 104, 148, 45, 173, 56, 141, 151, 130, 62, 154, 43, 97, 94, 33, 163, 172, 99, 115, 64, 118, 138, 127, 101, 6, 23, 16, 11, 0, 17, 143, 136, 9, 128, 100, 114, 67, 112, 98, 165, 110, 5, 2, 142, 169, 179, 47, 37, 83, 70, 164, 131, 155, 55, 123, 168, 159, and 149.

FIG. 233 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 233, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 141, 86, 22, 20, 176, 21, 37, 82, 6, 122, 130, 40, 62, 44, 24, 117, 8, 145, 36, 79, 172, 149, 127, 163, 9, 160, 73, 100, 16, 153, 124, 110, 49, 154, 152, 4, 168, 54, 177, 158, 113, 57, 2, 102, 161, 147, 18, 103, 1, 41, 104, 144, 39, 105, 131, 77, 69, 108, 159, 61, 45, 156, 0, 83, 157, 119, 112, 118, 92, 109, 75, 67, 142, 96, 51, 139, 31, 166, 179, 89, 167, 23, 34, 60, 93, 165, 128, 90, 19, 33, 70, 173, 174, 129, 55, 98, 88, 97, 146, 123, 84, 111, 132, 71, 140, 136, 10, 115, 63, 46, 42, 50, 138, 81, 59, 53, 15, 52, 72, 164, 150, 29, 17, 91, 101, 14, 38, 35, 66, 64, 7, 125, 151, 56, 126, 171, 68, 121, 28, 65, 106, 78, 47, 143, 12, 169, 120, 27, 74, 48, 133, 43, 116, 137, 94, 3, 25, 134, 13, 107, 162, 32, 99, 85, 175, 80, 170, 5, 135, 178, 11, 26, 76, 95, 87, 155, 58, 30, 148, and 114.

According to the converted GW pattern (B) of FIG. 233, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 141, 70, 86, 173, 22, 174, 20, 129, 176, 55, 21, 98, 37, 88, 82, 97, 6, 146, 122, 123, 130, 84, 40, 111, 62, 132, 44, 71, 24, 140, 117, 136, 8, 10, 145, 115, 36, 63, 79, 46, 172, 42, 149, 50, 127, 138, 163, 81, 9, 59, 160, 53, 73, 15, 100, 52, 16, 72, 153, 164, 124, 150, 110, 29, 49, 17, 154, 91, 152, 101, 4, 14, 168, 38, 54, 35, 177, 66, 158, 64, 113, 7, 57, 125, 2, 151, 102, 56, 161, 126, 147, 171, 18, 68, 103, 121, 1, 28, 41, 65, 104, 106, 144, 78, 39, 47, 105, 143, 131, 12, 77, 169, 69, 120, 108, 27, 159, 74, 61, 48, 45, 133, 156, 43, 0, 116, 83, 137, 157, 94, 119, 3, 112, 25, 118, 134, 92, 13, 109, 107, 75, 162, 67, 32, 142, 99, 96, 85, 51, 175, 139, 80, 31, 170, 166, 5, 179, 135, 89, 178, 167, 11, 23, 26, 34, 76, 60, 95, 93, 87, 165, 155, 128, 58, 90, 30, 19, 148, 33, and 114.

FIG. 234 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 234, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 39, 47, 96, 176, 33, 75, 165, 38, 27, 58, 90, 76, 17, 46, 10, 91, 133, 69, 171, 32, 117, 78, 13, 146, 101, 36, 0, 138, 25, 77, 122, 49, 14, 125, 140, 93, 130, 2, 104, 102, 128, 4, 111, 151, 84, 167, 35, 127, 156, 55, 82, 85, 66, 114, 8, 147, 115, 113, 5, 31, 100, 106, 48, 52, 67, 107, 18, 126, 112, 50, 9, 143, 28, 160, 71, 79, 43, 98, 86, 94, 64, 3, 166, 105, 103, 118, 63, 51, 139, 172, 141, 175, 56, 74, 95, 29, 45, 129, 120, 168, 92, 150, 7, 162, 153, 137, 108, 159, 157, 173, 23, 89, 132, 57, 37, 70, 134, 40, 21, 149, 80, 1, 121, 59, 110, 142, 152, 15, 154, 145, 12, 170, 54, 155, 99, 22, 123, 72, 177, 131, 116, 44, 158, 73, 11, 65, 164, 119, 174, 34, 83, 53, 24, 42, 60, 26, 161, 68, 178, 41, 148, 109, 87, 144, 135, 20, 62, 81, 169, 124, 6, 19, 30, 163, 61, 179, 136, 97, 16, and 88.

According to the converted GW pattern (B) of FIG. 234, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 39, 141, 47, 175, 96, 56, 176, 74, 33, 95, 75, 29, 165, 45, 38, 129, 27, 120, 58, 168, 90, 92, 76, 150, 17, 7, 46, 162, 10, 153, 91, 137, 133, 108, 69, 159, 171, 157, 32, 173, 117, 23, 78, 89, 13, 132, 146, 57, 101, 37, 36, 70, 0, 134, 138, 40, 25, 21, 77, 149, 122, 80, 49, 1, 14, 121, 125, 59, 140, 110, 93, 142, 130, 152, 2, 15, 104, 154, 102, 145, 128, 12, 4, 170, 111, 54, 151, 155, 84, 99, 167, 22, 35, 123, 127, 72, 156, 177, 55, 131, 82, 116, 85, 44, 66, 158, 114, 73, 8, 11, 147, 65, 115, 164, 113, 119, 5, 174, 31, 34, 100, 83, 106, 53, 48, 24, 52, 42, 67, 60, 107, 26, 18, 161, 126, 68, 112, 178, 50, 41, 9, 148, 143, 109, 28, 87, 160, 144, 71, 135, 79, 20, 43, 62, 98, 81, 86, 169, 94, 124, 64, 6, 3, 19, 166, 30, 105, 163, 103, 61, 118, 179, 63, 136, 51, 97, 139, 16, 172, and 88.

FIG. 235 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 6/15.

According to the original GW pattern (A) of FIG. 235, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107, 31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129, 52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97, 33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17, 15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130, 56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45, 78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96, 32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 235, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 4, 14, 5, 19, 10, 21, 12, 2, 20, 11, 6, 22, 18, 9, 13, 8, 17, 7, 15, 16, 1, 3, 29, 26, 28, 24, 23, 27, 25, 80, 67, 100, 116, 121, 66, 107, 104, 31, 44, 36, 50, 42, 47, 46, 84, 49, 76, 75, 65, 93, 130, 127, 56, 95, 128, 119, 77, 73, 39, 61, 94, 63, 87, 117, 120, 89, 62, 99, 88, 129, 74, 52, 35, 111, 110, 124, 131, 48, 98, 122, 60, 82, 37, 106, 45, 91, 78, 92, 125, 71, 41, 103, 34, 102, 118, 81, 38, 113, 72, 101, 108, 97, 58, 33, 43, 115, 109, 59, 57, 112, 105, 90, 68, 51, 86, 126, 79, 85, 96, 123, 32, 40, 114, 83, 64, 53, 55, 69, 30, 70, 54, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 236 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 7/15.

According to the original GW pattern (A) of FIG. 236, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 152, 172, 113, 167, 100, 163, 159, 144, 114, 47, 161, 125, 99, 89, 179, 123, 149, 177, 1, 132, 37, 26, 16, 57, 166, 81, 133, 112, 33, 151, 117, 83, 52, 178, 85, 124, 143, 28, 59, 130, 31, 157, 170, 44, 61, 102, 155, 111, 153, 55, 54, 176, 17, 68, 169, 20, 104, 38, 147, 7, 174, 6, 90, 15, 56, 120, 13, 34, 48, 122, 110, 154, 76, 64, 75, 84, 162, 77, 103, 156, 128, 150, 87, 27, 42, 3, 23, 96, 171, 145, 91, 24, 78, 5, 69, 175, 8, 29, 106, 137, 131, 43, 93, 160, 108, 164, 12, 140, 71, 63, 141, 109, 129, 82, 80, 173, 105, 9, 66, 65, 92, 32, 41, 72, 74, 4, 36, 94, 67, 158, 10, 88, 142, 45, 126, 2, 86, 118, 73, 79, 121, 148, 95, 70, 51, 53, 21, 115, 135, 25, 168, 11, 136, 18, 138, 134, 119, 146, 0, 97, 22, 165, 40, 19, 60, 46, 14, 49, 139, 58, 101, 39, 116, 127, 30, 98, 50, 107, 35, and 62.

According to the converted GW pattern (B) of FIG. 236, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 152, 91, 172, 24, 113, 78, 167, 5, 100, 69, 163, 175, 159, 8, 144, 29, 114, 106, 47, 137, 161, 131, 125, 43, 99, 93, 89, 160, 179, 108, 123, 164, 149, 12, 177, 140, 1, 71, 132, 63, 37, 141, 26, 109, 16, 129, 57, 82, 166, 80, 81, 173, 133, 105, 112, 9, 33, 66, 151, 65, 117, 92, 83, 32, 52, 41, 178, 72, 85, 74, 124, 4, 143, 36, 28, 94, 59, 67, 130, 158, 31, 10, 157, 88, 170, 142, 44, 45, 61, 126, 102, 2, 155, 86, 111, 118, 153, 73, 55, 79, 54, 121, 176, 148, 17, 95, 68, 70, 169, 51, 20, 53, 104, 21, 38, 115, 147, 135, 7, 25, 174, 168, 6, 11, 90, 136, 15, 18, 56, 138, 120, 134, 13, 119, 34, 146, 48, 0, 122, 97, 110, 22, 154, 165, 76, 40, 64, 19, 75, 60, 84, 46, 162, 14, 77, 49, 103, 139, 156, 58, 128, 101, 150, 39, 87, 116, 27, 127, 42, 30, 3, 98, 23, 50, 96, 107, 171, 35, 145, and 62.

FIG. 237 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 237, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 237, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 238 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 9/15.

According to the original GW pattern (A) of FIG. 238, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 238, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 239 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 239, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 239, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 240 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 11/15.

According to the original GW pattern (A) of FIG. 240, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107, 31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129, 52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97, 33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17, 15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130, 56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45, 78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96, 32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 240, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 4, 14, 5, 19, 10, 21, 12, 2, 20, 11, 6, 22, 18, 9, 13, 8, 17, 7, 15, 16, 1, 3, 29, 26, 28, 24, 23, 27, 25, 80, 67, 100, 116, 121, 66, 107, 104, 31, 44, 36, 50, 42, 47, 46, 84, 49, 76, 75, 65, 93, 130, 127, 56, 95, 128, 119, 77, 73, 39, 61, 94, 63, 87, 117, 120, 89, 62, 99, 88, 129, 74, 52, 35, 111, 110, 124, 131, 48, 98, 122, 60, 82, 37, 106, 45, 91, 78, 92, 125, 71, 41, 103, 34, 102, 118, 81, 38, 113, 72, 101, 108, 97, 58, 33, 43, 115, 109, 59, 57, 112, 105, 90, 68, 51, 86, 126, 79, 85, 96, 123, 32, 40, 114, 83, 64, 53, 55, 69, 30, 70, 54, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 241 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 241, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 241, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 242 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 242, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, and 179.

According to the converted GW pattern (B) of FIG. 242, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 243 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 243, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 5, 58, 29, 154, 125, 34, 0, 169, 80, 59, 13, 42, 77, 167, 32, 87, 24, 92, 124, 143, 114, 120, 166, 138, 64, 136, 149, 57, 18, 101, 119, 35, 33, 113, 75, 108, 104, 3, 27, 39, 172, 159, 129, 62, 146, 142, 19, 147, 111, 70, 74, 79, 10, 132, 1, 161, 155, 90, 15, 133, 47, 112, 84, 28, 160, 117, 150, 49, 7, 81, 44, 63, 118, 4, 158, 148, 82, 69, 36, 162, 86, 71, 22, 26, 61, 40, 126, 170, 177, 23, 91, 68, 56, 110, 21, 93, 107, 85, 20, 128, 109, 66, 83, 12, 179, 141, 97, 78, 157, 72, 130, 99, 165, 45, 11, 152, 168, 14, 16, 2, 137, 140, 121, 173, 50, 55, 94, 144, 73, 51, 98, 174, 178, 17, 100, 9, 122, 54, 38, 156, 131, 127, 164, 102, 116, 176, 30, 37, 139, 95, 43, 135, 53, 89, 106, 171, 76, 175, 153, 96, 151, 115, 52, 6, 123, 134, 31, 103, 163, 65, 105, 48, 25, 8, 60, 67, 88, 46, 41, and 145.

According to the converted GW pattern (B) of FIG. 243, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 5, 142, 91, 9, 58, 19, 68, 122, 29, 147, 56, 54, 154, 111, 110, 38, 125, 70, 21, 156, 34, 74, 93, 131, 0, 79, 107, 127, 169, 10, 85, 164, 80, 132, 20, 102, 59, 1, 128, 116, 13, 161, 109, 176, 42, 155, 66, 30, 77, 90, 83, 37, 167, 15, 12, 139, 32, 133, 179, 95, 87, 47, 141, 43, 24, 112, 97, 135, 92, 84, 78, 53, 124, 28, 157, 89, 143, 160, 72, 106, 114, 117, 130, 171, 120, 150, 99, 76, 166, 49, 165, 175, 138, 7, 45, 153, 64, 81, 11, 96, 136, 44, 152, 151, 149, 63, 168, 115, 57, 118, 14, 52, 18, 4, 16, 6, 101, 158, 2, 123, 119, 148, 137, 134, 35, 82, 140, 31, 33, 69, 121, 103, 113, 36, 173, 163, 75, 162, 50, 65, 108, 86, 55, 105, 104, 71, 94, 48, 3, 22, 144, 25, 27, 26, 73, 8, 39, 61, 51, 60, 172, 40, 98, 67, 159, 126, 174, 88, 129, 170, 178, 46, 62, 177, 17, 41, 146, 23, 100, and 145.

FIG. 244 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 244, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 52, 92, 175, 26, 45, 81, 117, 74, 119, 147, 120, 135, 144, 87, 3, 51, 20, 170, 143, 125, 15, 39, 5, 174, 79, 16, 176, 44, 19, 69, 11, 111, 121, 37, 160, 88, 50, 76, 129, 138, 157, 86, 113, 164, 142, 98, 9, 93, 166, 78, 73, 167, 168, 40, 131, 27, 89, 156, 177, 171, 116, 152, 0, 127, 36, 8, 153, 59, 75, 13, 105, 55, 122, 132, 172, 2, 58, 126, 162, 30, 77, 158, 17, 96, 100, 42, 63, 134, 154, 6, 90, 128, 83, 60, 146, 124, 178, 99, 123, 108, 133, 159, 151, 145, 61, 53, 68, 31, 41, 94, 35, 21, 49, 82, 80, 4, 155, 7, 57, 95, 62, 56, 65, 140, 163, 148, 23, 161, 169, 47, 67, 139, 72, 43, 110, 46, 150, 109, 115, 32, 14, 179, 85, 165, 112, 25, 64, 173, 10, 102, 114, 71, 66, 84, 24, 141, 29, 104, 107, 54, 12, 91, 1, 118, 136, 18, 101, 149, 130, 103, 106, 38, 70, 48, 28, 137, 97, 34, 22, and 33.

According to the converted GW pattern (B) of FIG. 244, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 52, 98, 90, 46, 92, 9, 128, 150, 175, 93, 83, 109, 26, 166, 60, 115, 45, 78, 146, 32, 81, 73, 124, 14, 117, 167, 178, 179, 74, 168, 99, 85, 119, 40, 123, 165, 147, 131, 108, 112, 120, 27, 133, 25, 135, 89, 159, 64, 144, 156, 151, 173, 87, 177, 145, 10, 3, 171, 61, 102, 51, 116, 53, 114, 20, 152, 68, 71, 170, 0, 31, 66, 143, 127, 41, 84, 125, 36, 94, 24, 15, 8, 35, 141, 39, 153, 21, 29, 5, 59, 49, 104, 174, 75, 82, 107, 79, 13, 80, 54, 16, 105, 4, 12, 176, 55, 155, 91, 44, 122, 7, 1, 19, 132, 57, 118, 69, 172, 95, 136, 11, 2, 62, 18, 111, 58, 56, 101, 121, 126, 65, 149, 37, 162, 140, 130, 160, 30, 163, 103, 88, 77, 148, 106, 50, 158, 23, 38, 76, 17, 161, 70, 129, 96, 169, 48, 138, 100, 47, 28, 157, 42, 67, 137, 86, 63, 139, 97, 113, 134, 72, 34, 164, 154, 43, 22, 142, 6, 110, and 33.

FIG. 245 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 245, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 165, 8, 136, 2, 58, 30, 127, 64, 38, 164, 123, 45, 78, 17, 47, 105, 159, 134, 124, 147, 148, 109, 67, 98, 157, 57, 156, 50, 104, 92, 163, 72, 125, 36, 14, 55, 48, 1, 149, 33, 110, 6, 130, 140, 89, 77, 22, 171, 139, 112, 113, 152, 16, 7, 85, 11, 28, 153, 73, 62, 44, 135, 116, 4, 61, 117, 53, 111, 178, 94, 81, 68, 114, 173, 75, 101, 88, 65, 99, 126, 141, 43, 15, 18, 90, 35, 24, 142, 25, 120, 19, 154, 0, 174, 93, 167, 150, 107, 86, 129, 175, 87, 21, 66, 106, 82, 179, 118, 41, 95, 145, 37, 23, 168, 166, 49, 103, 108, 56, 91, 69, 128, 121, 96, 133, 100, 161, 143, 119, 102, 59, 20, 40, 70, 79, 80, 51, 13, 177, 131, 132, 176, 155, 31, 63, 5, 162, 76, 42, 160, 115, 71, 158, 54, 137, 146, 32, 169, 122, 138, 84, 74, 60, 34, and 27.

According to the converted GW pattern (B) of FIG. 245, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 165, 163, 101, 69, 8, 72, 88, 128, 136, 125, 65, 121, 2, 36, 99, 96, 58, 14, 126, 133, 30, 55, 141, 100, 127, 48, 43, 161, 64, 1, 15, 143, 38, 149, 18, 119, 164, 33, 90, 102, 123, 110, 35, 59, 45, 6, 24, 20, 78, 130, 142, 40, 17, 140, 25, 70, 47, 89, 120, 79, 105, 77, 19, 80, 159, 22, 154, 51, 134, 171, 0, 13, 124, 139, 174, 177, 147, 112, 93, 131, 148, 113, 167, 132, 109, 152, 150, 176, 67, 16, 107, 155, 98, 7, 86, 31, 157, 85, 129, 63, 57, 11, 175, 5, 156, 28, 87, 162, 170, 153, 21, 76, 46, 73, 66, 42, 12, 62, 106, 160, 172, 44, 82, 115, 29, 135, 179, 71, 9, 116, 118, 158, 3, 4, 41, 54, 144, 61, 95, 137, 97, 117, 145, 146, 83, 53, 37, 32, 151, 111, 23, 169, 26, 178, 168, 122, 52, 94, 166, 138, 10, 81, 49, 84, 39, 68, 103, 74, 50, 114, 108, 60, 104, 173, 56, 34, 92, 75, 91, and 27.

FIG. 246 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 5/15.

According to the original GW pattern (B) of FIG. 246, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 129, 65, 160, 140, 32, 50, 162, 86, 177, 57, 157, 9, 134, 104, 24, 7, 122, 46, 17, 77, 31, 92, 163, 148, 133, 99, 18, 0, 167, 101, 110, 135, 124, 71, 107, 5, 123, 69, 108, 141, 179, 96, 113, 83, 176, 52, 117, 81, 125, 59, 15, 137, 170, 63, 112, 88, 34, 61, 106, 3, 42, 100, 152, 87, 171, 72, 161, 4, 178, 64, 150, 10, 128, 49, 26, 75, 41, 102, 28, 2, 168, 93, 156, 12, 38, 45, 151, 142, 44, 66, 25, 139, 173, 51, 29, 147, 175, 90, 164, 80, 131, 58, 114, 145, 121, 70, 115, 146, 120, 55, 158, 8, 39, 97, 159, 138, 33, 47, 116, 79, 174, 74, 21, 6, 130, 54, 109, 76, 35, 98, 155, 144, 36, 94, 23, 78, 165, 56, 154, 89, 132, 67, 119, 143, 40, 53, 20, 136, 172, 91, 27, 13, 127, 73, 105, 85, 30, 103, 19, 84, 37, 48, 153, 11, 166, 60, 111, 14, 169, 95, 118, 1, 126, 68, 22, 149, 43, 62, 16, and 82.

According to the converted GW pattern (A) of FIG. 246, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 129, 32, 177, 134, 122, 31, 133, 167, 124, 123, 179, 176, 125, 170, 34, 42, 171, 178, 128, 41, 168, 38, 44, 173, 175, 131, 121, 120, 39, 33, 174, 130, 35, 36, 165, 132, 40, 172, 127, 30, 37, 166, 169, 126, 43, 65, 50, 57, 104, 46, 92, 99, 101, 71, 69, 96, 52, 59, 63, 61, 100, 72, 64, 49, 102, 93, 45, 66, 51, 90, 58, 70, 55, 97, 47, 74, 54, 98, 94, 56, 67, 53, 91, 73, 103, 48, 60, 95, 68, 62, 160, 162, 157, 24, 17, 163, 18, 110, 107, 108, 113, 117, 15, 112, 106, 152, 161, 150, 26, 28, 156, 151, 25, 29, 164, 114, 115, 158, 159, 116, 21, 109, 155, 23, 154, 119, 20, 27, 105, 19, 153, 111, 118, 22, 16, 140, 86, 9, 7, 77, 148, 0, 135, 5, 141, 83, 81, 137, 88, 3, 87, 4, 10, 75, 2, 12, 142, 139, 147, 80, 145, 146, 8, 138, 79, 6, 76, 144, 78, 89, 143, 136, 13, 85, 84, 11, 14, 1, 149, and 82.

FIG. 247 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 6/15.

According to the original GW pattern (A) of FIG. 247, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 55, 146, 83, 52, 62, 176, 160, 68, 53, 56, 81, 97, 79, 113, 163, 61, 58, 69, 133, 108, 66, 71, 86, 144, 57, 67, 116, 59, 70, 156, 172, 65, 149, 155, 82, 138, 136, 141, 111, 96, 170, 90, 140, 64, 159, 15, 14, 37, 54, 44, 63, 43, 18, 47, 7, 25, 34, 29, 30, 26, 39, 16, 41, 45, 36, 0, 23, 32, 28, 27, 38, 48, 33, 22, 49, 51, 60, 46, 21, 4, 3, 20, 13, 50, 35, 24, 40, 17, 42, 6, 112, 93, 127, 101, 94, 115, 105, 31, 19, 177, 74, 10, 145, 162, 102, 120, 126, 95, 73, 152, 129, 174, 125, 72, 128, 78, 171, 8, 142, 178, 154, 85, 107, 75, 12, 9, 151, 77, 117, 109, 80, 106, 134, 98, 1, 122, 173, 161, 150, 110, 175, 166, 131, 119, 103, 139, 148, 157, 114, 147, 87, 158, 121, 164, 104, 89, 179, 123, 118, 99, 88, 11, 92, 165, 84, 168, 124, 169, 2, 130, 167, 153, 137, 143, 91, 100, 5, 76, 132, and 135.

According to the converted GW pattern (B) of FIG. 247, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 55, 15, 112, 122, 146, 14, 93, 173, 83, 37, 127, 161, 52, 54, 101, 150, 62, 44, 94, 110, 176, 63, 115, 175, 160, 43, 105, 166, 68, 18, 31, 131, 53, 47, 19, 119, 56, 7, 177, 103, 81, 25, 74, 139, 97, 34, 10, 148, 79, 29, 145, 157, 113, 30, 162, 114, 163, 26, 102, 147, 61, 39, 120, 87, 58, 16, 126, 158, 69, 41, 95, 121, 133, 45, 73, 164, 108, 36, 152, 104, 66, 0, 129, 89, 71, 23, 174, 179, 86, 32, 125, 123, 144, 28, 72, 118, 57, 27, 128, 99, 67, 38, 78, 88, 116, 48, 171, 11, 59, 33, 8, 92, 70, 22, 142, 165, 156, 49, 178, 84, 172, 51, 154, 168, 65, 60, 85, 124, 149, 46, 107, 169, 155, 21, 75, 2, 82, 4, 12, 130, 138, 3, 9, 167, 136, 20, 151, 153, 141, 13, 77, 137, 111, 50, 117, 143, 96, 35, 109, 91, 170, 24, 80, 100, 90, 40, 106, 5, 140, 17, 134, 76, 64, 42, 98, 132, 159, 6, 1, and 135.

FIG. 248 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 7/15.

According to the original GW pattern (A) of FIG. 248, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 174, 148, 56, 168, 38, 7, 110, 9, 42, 153, 160, 15, 46, 21, 121, 88, 114, 85, 13, 83, 74, 81, 70, 27, 119, 118, 144, 31, 80, 109, 73, 141, 93, 45, 16, 77, 108, 57, 36, 78, 124, 79, 169, 143, 6, 58, 75, 67, 5, 104, 125, 140, 172, 8, 39, 17, 29, 159, 86, 87, 41, 99, 89, 47, 128, 43, 161, 154, 101, 163, 116, 94, 120, 71, 158, 145, 37, 112, 68, 95, 1, 113, 64, 72, 90, 92, 35, 167, 44, 149, 66, 28, 82, 178, 176, 152, 23, 115, 130, 98, 123, 102, 24, 129, 150, 34, 136, 171, 54, 107, 2, 3, 60, 69, 10, 117, 91, 157, 33, 105, 155, 62, 162, 40, 127, 14, 165, 26, 52, 19, 48, 137, 4, 22, 122, 173, 18, 11, 111, 106, 76, 53, 61, 147, 97, 175, 32, 59, 166, 179, 135, 177, 103, 100, 139, 50, 146, 134, 133, 96, 49, 126, 151, 84, 156, 30, 138, 164, 132, 12, 0, 20, 63, 170, 142, 65, 55, 25, 51, and 131.

According to the converted GW pattern (B) of FIG. 248, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 174, 58, 66, 173, 148, 75, 28, 18, 56, 67, 82, 11, 168, 5, 178, 111, 38, 104, 176, 106, 7, 125, 152, 76, 110, 140, 23, 53, 9, 172, 115, 61, 42, 8, 130, 147, 153, 39, 98, 97, 160, 17, 123, 175, 15, 29, 102, 32, 46, 159, 24, 59, 21, 86, 129, 166, 121, 87, 150, 179, 88, 41, 34, 135, 114, 99, 136, 177, 85, 89, 171, 103, 13, 47, 54, 100, 83, 128, 107, 139, 74, 43, 2, 50, 81, 161, 3, 146, 70, 154, 60, 134, 27, 101, 69, 133, 119, 163, 10, 96, 118, 116, 117, 49, 144, 94, 91, 126, 31, 120, 157, 151, 80, 71, 33, 84, 109, 158, 105, 156, 73, 145, 155, 30, 141, 37, 62, 138, 93, 112, 162, 164, 45, 68, 40, 132, 16, 95, 127, 12, 77, 1, 14, 0, 108, 113, 165, 20, 57, 64, 26, 63, 36, 72, 52, 170, 78, 90, 19, 142, 124, 92, 48, 65, 79, 35, 137, 55, 169, 167, 4, 25, 143, 44, 22, 51, 6, 149, 122, and 131.

FIG. 249 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 8/15.

According to the original GW pattern (B) of FIG. 249, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 71, 81, 170, 101, 143, 77, 128, 112, 155, 41, 40, 54, 57, 28, 179, 114, 97, 13, 18, 151, 91, 88, 79, 92, 137, 27, 122, 107, 135, 82, 125, 103, 74, 36, 9, 93, 0, 86, 63, 158, 148, 25, 167, 116, 70, 43, 102, 106, 149, 24, 169, 113, 127, 34, 165, 100, 136, 75, 134, 156, 96, 84, 178, 150, 140, 20, 126, 73, 68, 130, 121, 48, 53, 22, 129, 99, 11, 33, 124, 157, 161, 29, 123, 160, 55, 26, 168, 98, 67, 15, 7, 94, 144, 1, 61, 65, 146, 42, 172, 115, 59, 76, 4, 162, 39, 85, 12, 72, 58, 44, 132, 47, 141, 35, 176, 104, 139, 80, 6, 95, 87, 90, 173, 163, 69, 32, 8, 154, 145, 23, 177, 111, 60, 38, 171, 62, 46, 21, 5, 153, 49, 78, 2, 109, 147, 89, 166, 152, 138, 31, 14, 131, 50, 37, 16, 117, 66, 19, 10, 159, 142, 105, 3, 164, 51, 83, 174, 108, 52, 17, 64, 119, 45, 133, 175, 110, 56, 30, 120, and 118.

According to the converted GW pattern (A) of FIG. 249, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 71, 143, 155, 57, 97, 91, 137, 135, 74, 0, 148, 70, 149, 127, 136, 96, 140, 68, 53, 11, 161, 55, 67, 144, 146, 59, 39, 58, 141, 139, 87, 69, 145, 60, 46, 49, 147, 138, 50, 66, 142, 51, 52, 45, 56, 81, 77, 41, 28, 13, 88, 27, 82, 36, 86, 25, 43, 24, 34, 75, 84, 20, 130, 22, 33, 29, 26, 15, 1, 42, 76, 85, 44, 35, 80, 90, 32, 23, 38, 21, 78, 89, 31, 37, 19, 105, 83, 17, 133, 30, 170, 128, 40, 179, 18, 79, 122, 125, 9, 63, 167, 102, 169, 165, 134, 178, 126, 121, 129, 124, 123, 168, 7, 61, 172, 4, 12, 132, 176, 6, 173, 8, 177, 171, 5, 2, 166, 14, 16, 10, 3, 174, 64, 175, 120, 101, 112, 54, 114, 151, 92, 107, 103, 93, 158, 116, 106, 113, 100, 156, 150, 73, 48, 99, 157, 160, 98, 94, 65, 115, 162, 72, 47, 104, 95, 163, 154, 111, 62, 153, 109, 152, 131, 117, 159, 164, 108, 119, 110, and 118.

FIG. 250 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 250, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 23, 89, 10, 142, 19, 41, 1, 146, 68, 87, 9, 51, 114, 92, 121, 69, 107, 97, 166, 162, 55, 174, 126, 149, 110, 128, 172, 28, 111, 78, 82, 120, 71, 52, 5, 141, 29, 30, 132, 148, 72, 85, 17, 160, 156, 154, 131, 164, 65, 76, 125, 50, 16, 130, 129, 143, 133, 98, 0, 42, 63, 83, 173, 49, 74, 43, 8, 147, 61, 36, 167, 119, 27, 86, 102, 48, 115, 99, 38, 163, 73, 101, 4, 153, 118, 90, 124, 151, 66, 93, 123, 157, 24, 44, 168, 80, 15, 39, 178, 45, 21, 37, 11, 136, 113, 77, 122, 158, 64, 81, 6, 60, 54, 35, 13, 57, 171, 100, 117, 46, 62, 33, 175, 137, 59, 103, 127, 70, 108, 88, 179, 40, 112, 104, 170, 140, 67, 32, 105, 159, 26, 96, 169, 135, 109, 47, 177, 56, 116, 79, 106, 150, 25, 94, 134, 152, 22, 84, 176, 139, 20, 34, 165, 138, 7, 91, 12, 145, 58, 95, 2, 144, 53, 75, 14, 155, 18, 31, 3, and 161.

According to the converted GW pattern (A) of FIG. 250, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 23, 19, 68, 114, 107, 55, 110, 111, 71, 29, 72, 156, 65, 16, 133, 63, 74, 61, 27, 115, 73, 118, 66, 24, 15, 21, 113, 64, 54, 171, 62, 59, 108, 112, 67, 26, 109, 116, 25, 22, 20, 7, 58, 53, 18, 89, 41, 87, 92, 97, 174, 128, 78, 52, 30, 85, 154, 76, 130, 98, 83, 43, 36, 86, 99, 101, 90, 93, 44, 39, 37, 77, 81, 35, 100, 33, 103, 88, 104, 32, 96, 47, 79, 94, 84, 34, 91, 95, 75, 31, 10, 1, 9, 121, 166, 126, 172, 82, 5, 132, 17, 131, 125, 129, 0, 173, 8, 167, 102, 38, 4, 124, 123, 168, 178, 11, 122, 6, 13, 117, 175, 127, 179, 170, 105, 169, 177, 106, 134, 176, 165, 12, 2, 14, 3, 142, 146, 51, 69, 162, 149, 28, 120, 141, 148, 160, 164, 50, 143, 42, 49, 147, 119, 48, 163, 153, 151, 157, 80, 45, 136, 158, 60, 57, 46, 137, 70, 40, 140, 159, 135, 56, 150, 152, 139, 138, 145, 144, 155, and 161.

FIG. 251 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 251, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 68, 71, 54, 19, 25, 21, 102, 32, 105, 29, 16, 79, 53, 82, 107, 91, 67, 94, 85, 48, 83, 58, 42, 57, 28, 76, 31, 26, 96, 65, 119, 114, 109, 9, 125, 81, 43, 103, 93, 70, 46, 89, 112, 61, 45, 66, 38, 77, 115, 56, 87, 113, 100, 75, 72, 60, 47, 92, 36, 98, 4, 59, 6, 44, 20, 86, 3, 73, 95, 104, 8, 34, 0, 84, 111, 35, 30, 64, 55, 80, 40, 97, 101, 2, 69, 63, 74, 62, 118, 110, 159, 18, 50, 33, 7, 175, 51, 131, 106, 134, 88, 140, 117, 132, 147, 153, 116, 161, 10, 39, 126, 136, 90, 37, 174, 41, 158, 5, 120, 12, 52, 99, 146, 144, 78, 155, 128, 165, 141, 179, 150, 157, 171, 143, 108, 170, 22, 49, 11, 27, 160, 178, 133, 142, 121, 168, 173, 123, 13, 15, 154, 127, 139, 151, 163, 172, 138, 176, 145, 129, 162, 152, 177, 137, 149, 167, 1, 14, 169, 124, 148, 164, 130, 17, 156, 122, 23, 166, 135, and 24.

According to the converted GW pattern (B) of FIG. 251, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 68, 66, 159, 170, 71, 38, 18, 22, 54, 77, 50, 49, 19, 115, 33, 11, 25, 56, 7, 27, 21, 87, 175, 160, 102, 113, 51, 178, 32, 100, 131, 133, 105, 75, 106, 142, 29, 72, 134, 121, 16, 60, 88, 168, 79, 47, 140, 173, 53, 92, 117, 123, 82, 36, 132, 13, 107, 98, 147, 15, 91, 4, 153, 154, 67, 59, 116, 127, 94, 6, 161, 139, 85, 44, 10, 151, 48, 20, 39, 163, 83, 86, 126, 172, 58, 3, 136, 138, 42, 73, 90, 176, 57, 95, 37, 145, 28, 104, 174, 129, 76, 8, 41, 162, 31, 34, 158, 152, 26, 0, 5, 177, 96, 84, 120, 137, 65, 111, 12, 149, 119, 35, 52, 167, 114, 30, 99, 1, 109, 64, 146, 14, 9, 55, 144, 169, 125, 80, 78, 124, 81, 40, 155, 148, 43, 97, 128, 164, 103, 101, 165, 130, 93, 2, 141, 17, 70, 69, 179, 156, 46, 63, 150, 122, 89, 74, 157, 23, 112, 62, 171, 166, 61, 118, 143, 135, 45, 110, 108, and 24.

FIG. 252 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 11/15.

According to the original GW pattern (A) of FIG. 252, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, and 179.

According to the converted GW pattern (B) of FIG. 252, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 21, 20, 2, 19, 11, 18, 17, 5, 12, 10, 1, 3, 9, 13, 4, 14, 0, 16, 7, 22, 6, 8, 15, 28, 24, 26, 29, 23, 25, 27, 82, 109, 85, 54, 32, 51, 103, 111, 102, 108, 118, 52, 76, 131, 122, 44, 121, 33, 71, 87, 92, 84, 101, 113, 130, 88, 41, 115, 127, 64, 93, 58, 62, 63, 55, 116, 107, 59, 73, 49, 38, 57, 100, 77, 46, 97, 40, 95, 43, 98, 106, 86, 110, 48, 119, 30, 75, 31, 45, 78, 104, 99, 80, 81, 70, 37, 128, 56, 91, 72, 68, 125, 69, 39, 129, 53, 96, 74, 61, 89, 120, 66, 124, 94, 42, 60, 36, 50, 34, 67, 126, 123, 79, 47, 117, 65, 35, 112, 114, 83, 105, 90, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 253 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 253, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 120, 32, 38, 113, 71, 31, 65, 109, 36, 106, 134, 66, 29, 86, 136, 108, 83, 70, 79, 81, 105, 48, 30, 125, 107, 44, 99, 75, 64, 78, 51, 95, 88, 49, 60, 54, 122, 140, 137, 89, 74, 129, 82, 164, 59, 3, 67, 92, 98, 42, 77, 28, 121, 87, 18, 21, 93, 72, 2, 142, 112, 9, 50, 8, 90, 139, 14, 97, 63, 85, 104, 124, 52, 20, 118, 34, 5, 94, 41, 68, 80, 110, 12, 133, 131, 53, 116, 123, 96, 61, 111, 33, 173, 165, 175, 166, 169, 174, 159, 148, 158, 155, 145, 178, 126, 100, 154, 156, 179, 157, 46, 149, 171, 37, 153, 163, 152, 146, 177, 103, 160, 147, 76, 172, 144, 150, 132, 176, 168, 167, 162, 170, 138, 151, 161, 40, 26, 130, 119, 114, 117, 115, 84, 57, 62, 13, 47, 24, 0, 7, 10, 69, 19, 127, 17, 16, 27, 91, 4, 73, 35, 102, 15, 55, 23, 25, 11, 56, 45, 58, 128, 43, 135, 1, 143, 141, 6, 22, 101, and 39.

According to the converted GW pattern (B) of FIG. 253, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 120, 3, 111, 40, 32, 67, 33, 26, 38, 92, 173, 130, 113, 98, 165, 119, 71, 42, 175, 114, 31, 77, 166, 117, 65, 28, 169, 115, 109, 121, 174, 84, 36, 87, 159, 57, 106, 18, 148, 62, 134, 21, 158, 13, 66, 93, 155, 47, 29, 72, 145, 24, 86, 2, 178, 0, 136, 142, 126, 7, 108, 112, 100, 10, 83, 9, 154, 69, 70, 50, 156, 19, 79, 8, 179, 127, 81, 90, 157, 17, 105, 139, 46, 16, 48, 14, 149, 27, 30, 97, 171, 91, 125, 63, 37, 4, 107, 85, 153, 73, 44, 104, 163, 35, 99, 124, 152, 102, 75, 52, 146, 15, 64, 20, 177, 55, 78, 118, 103, 23, 51, 34, 160, 25, 95, 5, 147, 11, 88, 94, 76, 56, 49, 41, 172, 45, 60, 68, 144, 58, 54, 80, 150, 128, 122, 110, 132, 43, 140, 12, 176, 135, 137, 133, 168, 1, 89, 131, 167, 143, 74, 53, 162, 141, 129, 116, 170, 6, 82, 123, 138, 22, 164, 96, 151, 101, 59, 61, 161, and 39.

FIG. 254 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 254, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, and 179.

According to the converted GW pattern (B) of FIG. 254, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 255 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 255, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 57, 149, 83, 142, 29, 20, 30, 52, 5, 100, 156, 22, 130, 167, 121, 126, 137, 158, 132, 82, 138, 128, 89, 88, 162, 32, 107, 3, 97, 166, 125, 129, 1, 6, 68, 148, 40, 87, 0, 80, 49, 24, 78, 101, 43, 112, 75, 172, 23, 154, 12, 146, 19, 135, 48, 170, 123, 147, 95, 91, 13, 35, 127, 61, 60, 139, 44, 59, 55, 109, 157, 177, 153, 165, 66, 152, 77, 98, 131, 11, 81, 62, 175, 141, 171, 51, 155, 76, 150, 174, 58, 143, 37, 63, 31, 41, 140, 118, 94, 27, 10, 70, 56, 93, 176, 124, 151, 106, 46, 163, 179, 4, 18, 144, 178, 161, 145, 71, 114, 7, 105, 133, 84, 86, 17, 21, 28, 54, 74, 65, 110, 122, 169, 64, 111, 119, 42, 85, 73, 8, 116, 79, 120, 69, 53, 115, 67, 104, 16, 173, 92, 15, 159, 134, 99, 96, 117, 38, 9, 26, 164, 47, 103, 113, 136, 168, 102, 14, 45, 72, 25, 50, 34, 36, 90, 160, 2, 33, 39, and 108.

According to the converted GW pattern (B) of FIG. 255, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 57, 125, 13, 58, 105, 92, 149, 129, 35, 143, 133, 15, 83, 1, 127, 37, 84, 159, 142, 6, 61, 63, 86, 134, 29, 68, 60, 31, 17, 99, 20, 148, 139, 41, 21, 96, 30, 40, 44, 140, 28, 117, 52, 87, 59, 118, 54, 38, 5, 0, 55, 94, 74, 9, 100, 80, 109, 27, 65, 26, 156, 49, 157, 10, 110, 164, 22, 24, 177, 70, 122, 47, 130, 78, 153, 56, 169, 103, 167, 101, 165, 93, 64, 113, 121, 43, 66, 176, 111, 136, 126, 112, 152, 124, 119, 168, 137, 75, 77, 151, 42, 102, 158, 172, 98, 106, 85, 14, 132, 23, 131, 46, 73, 45, 82, 154, 11, 163, 8, 72, 138, 12, 81, 179, 116, 25, 128, 146, 62, 4, 79, 50, 89, 19, 175, 18, 120, 34, 88, 135, 141, 144, 69, 36, 162, 48, 171, 178, 53, 90, 32, 170, 51, 161, 115, 160, 107, 123, 155, 145, 67, 2, 3, 147, 76, 71, 104, 33, 97, 95, 150, 114, 16, 39, 166, 91, 174, 7, 173, and 108.

FIG. 256 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 256, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 74, 72, 104, 62, 122, 35, 130, 0, 95, 150, 139, 151, 133, 109, 31, 59, 18, 148, 9, 105, 57, 132, 102, 100, 115, 101, 7, 21, 141, 30, 8, 1, 93, 92, 163, 108, 52, 159, 24, 89, 117, 88, 178, 113, 98, 179, 144, 156, 54, 164, 12, 63, 39, 22, 25, 137, 13, 41, 44, 80, 87, 111, 145, 23, 85, 166, 83, 55, 154, 20, 84, 58, 26, 126, 170, 103, 11, 33, 172, 155, 116, 169, 142, 70, 161, 47, 3, 162, 77, 19, 28, 97, 124, 6, 168, 107, 60, 76, 143, 121, 42, 157, 65, 43, 173, 56, 171, 90, 131, 119, 94, 5, 68, 138, 149, 73, 67, 53, 61, 4, 86, 99, 75, 36, 15, 48, 177, 167, 174, 51, 176, 81, 120, 158, 123, 34, 49, 128, 10, 134, 147, 96, 160, 50, 146, 16, 38, 78, 91, 152, 46, 127, 27, 175, 135, 79, 125, 82, 2, 129, 153, 14, 40, 32, 114, 106, 17, 110, 140, 71, 136, 112, 45, 64, 29, 69, 118, 66, 37, and 165.

According to the converted GW pattern (B) of FIG. 256, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 74, 8, 87, 28, 86, 46, 72, 1, 111, 97, 99, 127, 104, 93, 145, 124, 75, 27, 62, 92, 23, 6, 36, 175, 122, 163, 85, 168, 15, 135, 35, 108, 166, 107, 48, 79, 130, 52, 83, 60, 177, 125, 0, 159, 55, 76, 167, 82, 95, 24, 154, 143, 174, 2, 150, 89, 20, 121, 51, 129, 139, 117, 84, 42, 176, 153, 151, 88, 58, 157, 81, 14, 133, 178, 26, 65, 120, 40, 109, 113, 126, 43, 158, 32, 31, 98, 170, 173, 123, 114, 59, 179, 103, 56, 34, 106, 18, 144, 11, 171, 49, 17, 148, 156, 33, 90, 128, 110, 9, 54, 172, 131, 10, 140, 105, 164, 155, 119, 134, 71, 57, 12, 116, 94, 147, 136, 132, 63, 169, 5, 96, 112, 102, 39, 142, 68, 160, 45, 100, 22, 70, 138, 50, 64, 115, 25, 161, 149, 146, 29, 101, 137, 47, 73, 16, 69, 7, 13, 3, 67, 38, 118, 21, 41, 162, 53, 78, 66, 141, 44, 77, 61, 91, 37, 30, 80, 19, 4, 152, and 165.

FIG. 257 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 257, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 141, 80, 47, 89, 44, 7, 46, 11, 175, 173, 99, 2, 155, 52, 86, 128, 174, 33, 170, 31, 35, 162, 64, 95, 92, 4, 16, 49, 137, 104, 29, 9, 60, 167, 50, 23, 43, 176, 121, 71, 132, 103, 144, 39, 12, 90, 114, 131, 106, 76, 118, 66, 24, 58, 122, 150, 57, 149, 93, 53, 14, 73, 165, 82, 126, 97, 59, 133, 154, 153, 72, 36, 5, 96, 120, 134, 101, 61, 115, 0, 28, 42, 18, 145, 156, 85, 146, 6, 161, 10, 22, 138, 127, 151, 87, 54, 20, 139, 140, 152, 13, 91, 111, 25, 123, 77, 78, 69, 3, 177, 41, 81, 19, 107, 45, 148, 70, 160, 51, 21, 116, 48, 157, 17, 125, 142, 83, 110, 37, 98, 179, 129, 168, 172, 1, 40, 166, 159, 147, 56, 100, 63, 26, 169, 135, 15, 75, 84, 163, 79, 143, 113, 94, 74, 102, 30, 38, 178, 68, 108, 136, 105, 158, 117, 34, 109, 67, 62, 32, 119, 124, 171, 8, 55, 65, 130, 88, 112, 27, and 164.

According to the converted GW pattern (B) of FIG. 257, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 141, 29, 14, 22, 116, 143, 80, 9, 73, 138, 48, 113, 47, 60, 165, 127, 157, 94, 89, 167, 82, 151, 17, 74, 44, 50, 126, 87, 125, 102, 7, 23, 97, 54, 142, 30, 46, 43, 59, 20, 83, 38, 11, 176, 133, 139, 110, 178, 175, 121, 154, 140, 37, 68, 173, 71, 153, 152, 98, 108, 99, 132, 72, 13, 179, 136, 2, 103, 36, 91, 129, 105, 155, 144, 5, 111, 168, 158, 52, 39, 96, 25, 172, 117, 86, 12, 120, 123, 1, 34, 128, 90, 134, 77, 40, 109, 174, 114, 101, 78, 166, 67, 33, 131, 61, 69, 159, 62, 170, 106, 115, 3, 147, 32, 31, 76, 0, 177, 56, 119, 35, 118, 28, 41, 100, 124, 162, 66, 42, 81, 63, 171, 64, 24, 18, 19, 26, 8, 95, 58, 145, 107, 169, 55, 92, 122, 156, 45, 135, 65, 4, 150, 85, 148, 15, 130, 16, 57, 146, 70, 75, 88, 49, 149, 6, 160, 84, 112, 137, 93, 161, 51, 163, 27, 104, 53, 10, 21, 79, and 164.

FIG. 258 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 258, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 166, 54, 6, 27, 141, 134, 58, 46, 55, 91, 56, 100, 172, 80, 18, 152, 12, 108, 170, 29, 144, 147, 106, 165, 17, 127, 57, 88, 35, 72, 5, 63, 118, 1, 85, 77, 61, 62, 84, 159, 92, 102, 98, 177, 132, 139, 59, 149, 11, 8, 154, 129, 33, 15, 143, 4, 95, 101, 53, 42, 40, 9, 111, 130, 123, 82, 81, 114, 119, 175, 157, 41, 38, 128, 161, 52, 142, 7, 26, 145, 2, 68, 28, 126, 121, 70, 16, 65, 83, 125, 50, 79, 37, 74, 164, 168, 160, 122, 60, 32, 24, 138, 75, 69, 0, 36, 97, 117, 14, 109, 173, 120, 112, 87, 176, 124, 151, 67, 13, 94, 105, 133, 64, 76, 153, 31, 136, 140, 150, 39, 96, 66, 3, 115, 20, 99, 171, 49, 25, 45, 22, 30, 156, 158, 163, 135, 21, 146, 90, 169, 78, 93, 178, 116, 19, 155, 110, 73, 104, 167, 44, 113, 162, 89, 47, 43, 86, 48, 107, 71, 137, 51, 174, 103, 131, 179, 148, 10, 23, and 34.

According to the converted GW pattern (B) of FIG. 258, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 166, 5, 40, 50, 105, 78, 54, 63, 9, 79, 133, 93, 6, 118, 111, 37, 64, 178, 27, 1, 130, 74, 76, 116, 141, 85, 123, 164, 153, 19, 134, 77, 82, 168, 31, 155, 58, 61, 81, 160, 136, 110, 46, 62, 114, 122, 140, 73, 55, 84, 119, 60, 150, 104, 91, 159, 175, 32, 39, 167, 56, 92, 157, 24, 96, 44, 100, 102, 41, 138, 66, 113, 172, 98, 38, 75, 3, 162, 80, 177, 128, 69, 115, 89, 18, 132, 161, 0, 20, 47, 152, 139, 52, 36, 99, 43, 12, 59, 142, 97, 171, 86, 108, 149, 7, 117, 49, 48, 170, 11, 26, 14, 25, 107, 29, 8, 145, 109, 45, 71, 144, 154, 2, 173, 22, 137, 147, 129, 68, 120, 30, 51, 106, 33, 28, 112, 156, 174, 165, 15, 126, 87, 158, 103, 17, 143, 121, 176, 163, 131, 127, 4, 70, 124, 135, 179, 57, 95, 16, 151, 21, 148, 88, 101, 65, 67, 146, 10, 35, 53, 83, 13, 90, 23, 72, 42, 125, 94, 169, and 34.

FIG. 259 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 6/15.

According to the original GW pattern (A) of FIG. 259, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 29, 17, 38, 37, 27, 43, 31, 35, 16, 46, 44, 9, 23, 1, 34, 45, 14, 18, 156, 19, 22, 40, 50, 24, 56, 49, 26, 42, 69, 47, 59, 61, 66, 52, 64, 65, 67, 54, 170, 68, 132, 51, 70, 41, 21, 5, 160, 7, 13, 55, 62, 53, 63, 58, 3, 167, 71, 57, 151, 60, 36, 25, 74, 39, 32, 72, 85, 86, 107, 113, 48, 88, 2, 129, 137, 20, 73, 166, 75, 77, 142, 174, 15, 149, 28, 145, 92, 169, 30, 133, 163, 119, 82, 176, 152, 134, 139, 148, 164, 99, 173, 104, 83, 106, 112, 135, 153, 0, 128, 144, 98, 171, 94, 97, 143, 110, 118, 127, 84, 79, 108, 126, 131, 93, 111, 91, 4, 125, 162, 157, 158, 109, 140, 123, 154, 150, 80, 11, 12, 146, 96, 81, 165, 8, 89, 138, 105, 141, 103, 6, 100, 161, 172, 78, 101, 115, 179, 147, 116, 136, 122, 87, 33, 130, 124, 175, 120, 90, 102, 10, 114, 159, 76, 177, 178, 121, 168, 95, 117, and 155.

According to the converted GW pattern (B) of FIG. 259, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 29, 59, 36, 163, 108, 100, 17, 61, 25, 119, 126, 161, 38, 66, 74, 82, 131, 172, 37, 52, 39, 176, 93, 78, 27, 64, 32, 152, 111, 101, 43, 65, 72, 134, 91, 115, 31, 67, 85, 139, 4, 179, 35, 54, 86, 148, 125, 147, 16, 170, 107, 164, 162, 116, 46, 68, 113, 99, 157, 136, 44, 132, 48, 173, 158, 122, 9, 51, 88, 104, 109, 87, 23, 70, 2, 83, 140, 33, 1, 41, 129, 106, 123, 130, 34, 21, 137, 112, 154, 124, 45, 5, 20, 135, 150, 175, 14, 160, 73, 153, 80, 120, 18, 7, 166, 0, 11, 90, 156, 13, 75, 128, 12, 102, 19, 55, 77, 144, 146, 10, 22, 62, 142, 98, 96, 114, 40, 53, 174, 171, 81, 159, 50, 63, 15, 94, 165, 76, 24, 58, 149, 97, 8, 177, 56, 3, 28, 143, 89, 178, 49, 167, 145, 110, 138, 121, 26, 71, 92, 118, 105, 168, 42, 57, 169, 127, 141, 95, 69, 151, 30, 84, 103, 117, 47, 60, 133, 79, 6, and 155.

FIG. 260 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 260, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 103, 36, 155, 175, 52, 130, 16, 178, 141, 86, 49, 129, 73, 84, 142, 177, 110, 8, 96, 77, 139, 167, 109, 2, 17, 37, 146, 169, 54, 134, 101, 78, 135, 70, 153, 6, 29, 41, 143, 63, 47, 124, 90, 31, 152, 98, 59, 133, 15, 79, 164, 67, 50, 128, 23, 34, 154, 69, 45, 9, 27, 35, 156, 170, 113, 127, 102, 82, 149, 176, 46, 13, 22, 30, 163, 60, 114, 11, 92, 44, 157, 74, 48, 132, 24, 87, 140, 66, 118, 123, 104, 89, 136, 64, 107, 14, 99, 43, 115, 71, 117, 12, 26, 38, 147, 62, 57, 131, 94, 33, 151, 172, 116, 10, 25, 75, 144, 179, 51, 120, 20, 80, 160, 174, 106, 1, 21, 88, 137, 61, 105, 5, 18, 32, 158, 72, 56, 125, 28, 42, 161, 168, 53, 7, 100, 40, 145, 171, 55, 3, 95, 83, 162, 173, 119, 126, 91, 39, 150, 165, 112, 122, 93, 76, 138, 166, 108, 121, 97, 81, 148, 65, 111, 4, 19, 85, 159, 68, 58, and 0.

According to the converted GW pattern (A) of FIG. 260, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 103, 16, 73, 96, 17, 101, 29, 90, 15, 23, 27, 102, 22, 92, 24, 104, 99, 26, 94, 25, 20, 21, 18, 28, 100, 95, 91, 93, 97, 19, 36, 178, 84, 77, 37, 78, 41, 31, 79, 34, 35, 82, 30, 44, 87, 89, 43, 38, 33, 75, 80, 88, 32, 42, 40, 83, 39, 76, 81, 85, 155, 141, 142, 139, 146, 135, 143, 152, 164, 154, 156, 149, 163, 157, 140, 136, 115, 147, 151, 144, 160, 137, 158, 161, 145, 162, 150, 138, 148, 159, 175, 86, 177, 167, 169, 70, 63, 98, 67, 69, 170, 176, 60, 74, 66, 64, 71, 62, 172, 179, 174, 61, 72, 168, 171, 173, 165, 166, 65, 68, 52, 49, 110, 109, 54, 153, 47, 59, 50, 45, 113, 46, 114, 48, 118, 107, 117, 57, 116, 51, 106, 105, 56, 53, 55, 119, 112, 108, 111, 58, 130, 129, 8, 2, 134, 6, 124, 133, 128, 9, 127, 13, 11, 132, 123, 14, 12, 131, 10, 120, 1, 5, 125, 7, 3, 126, 122, 121, 4, and 0.

FIG. 261 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 261, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 86, 71, 51, 48, 89, 94, 46, 81, 67, 49, 80, 37, 55, 61, 36, 57, 52, 92, 60, 82, 76, 72, 44, 42, 91, 62, 50, 90, 40, 78, 53, 58, 47, 85, 70, 4, 69, 43, 54, 84, 93, 38, 8, 64, 6, 18, 77, 95, 66, 59, 83, 73, 17, 87, 3, 75, 65, 88, 79, 14, 151, 117, 32, 22, 123, 30, 33, 162, 144, 9, 121, 108, 139, 142, 24, 34, 20, 157, 159, 138, 143, 29, 140, 163, 150, 175, 114, 31, 12, 35, 145, 28, 27, 26, 16, 98, 102, 103, 133, 161, 21, 25, 107, 153, 45, 156, 23, 125, 141, 56, 166, 5, 1, 170, 119, 68, 134, 41, 74, 179, 2, 129, 169, 101, 99, 109, 127, 168, 176, 11, 0, 122, 110, 113, 146, 132, 165, 19, 13, 39, 7, 164, 106, 172, 154, 149, 10, 173, 131, 167, 63, 147, 155, 100, 171, 158, 160, 15, 178, 148, 152, 104, 124, 177, 97, 130, 118, 137, 111, 126, 120, 105, 115, 136, 112, 96, 135, 116, 174, and 128.

According to the converted GW pattern (B) of FIG. 261, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 86, 53, 151, 145, 2, 63, 71, 58, 117, 28, 129, 147, 51, 47, 32, 27, 169, 155, 48, 85, 22, 26, 101, 100, 89, 70, 123, 16, 99, 171, 94, 4, 30, 98, 109, 158, 46, 69, 33, 102, 127, 160, 81, 43, 162, 103, 168, 15, 67, 54, 144, 133, 176, 178, 49, 84, 9, 161, 11, 148, 80, 93, 121, 21, 0, 152, 37, 38, 108, 25, 122, 104, 55, 8, 139, 107, 110, 124, 61, 64, 142, 153, 113, 177, 36, 6, 24, 45, 146, 97, 57, 18, 34, 156, 132, 130, 52, 77, 20, 23, 165, 118, 92, 95, 157, 125, 19, 137, 60, 66, 159, 141, 13, 111, 82, 59, 138, 56, 39, 126, 76, 83, 143, 166, 7, 120, 72, 73, 29, 5, 164, 105, 44, 17, 140, 1, 106, 115, 42, 87, 163, 170, 172, 136, 91, 3, 150, 119, 154, 112, 62, 75, 175, 68, 149, 96, 50, 65, 114, 134, 10, 135, 90, 88, 31, 41, 173, 116, 40, 79, 12, 74, 131, 174, 78, 14, 35, 179, 167, and 128.

FIG. 262 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 262, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 175, 60, 133, 11, 5, 4, 70, 97, 131, 80, 42, 136, 50, 104, 32, 75, 176, 87, 109, 61, 39, 107, 0, 172, 23, 90, 54, 160, 48, 173, 27, 100, 129, 14, 7, 142, 20, 103, 38, 126, 157, 144, 21, 64, 44, 79, 105, 146, 49, 93, 1, 84, 81, 145, 18, 15, 106, 91, 12, 169, 63, 71, 125, 37, 120, 138, 17, 113, 31, 130, 140, 8, 25, 74, 134, 115, 9, 171, 46, 68, 33, 116, 2, 179, 52, 92, 36, 78, 164, 177, 24, 72, 122, 118, 162, 121, 16, 73, 45, 53, 77, 110, 30, 66, 29, 76, 158, 148, 111, 94, 43, 83, 139, 10, 56, 98, 114, 117, 152, 174, 47, 62, 128, 85, 155, 178, 26, 96, 41, 82, 150, 143, 58, 69, 127, 86, 13, 141, 35, 101, 149, 108, 3, 154, 51, 95, 132, 135, 163, 137, 28, 102, 123, 112, 151, 167, 59, 19, 156, 119, 153, 168, 55, 65, 34, 6, 159, 170, 57, 67, 40, 89, 147, 165, 22, 99, 124, 88, 161, and 166.

According to the converted GW pattern (A) of FIG. 262, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 175, 70, 50, 109, 23, 27, 20, 21, 49, 18, 63, 17, 25, 46, 52, 24, 16, 30, 111, 56, 47, 26, 58, 35, 51, 28, 59, 55, 57, 22, 60, 97, 104, 61, 90, 100, 103, 64, 93, 15, 71, 113, 74, 68, 92, 72, 73, 66, 94, 98, 62, 96, 69, 101, 95, 102, 19, 65, 67, 99, 133, 131, 32, 39, 54, 129, 38, 44, 1, 106, 125, 31, 134, 33, 36, 122, 45, 29, 43, 114, 128, 41, 127, 149, 132, 123, 156, 34, 40, 124, 11, 80, 75, 107, 160, 14, 126, 79, 84, 91, 37, 130, 115, 116, 78, 118, 53, 76, 83, 117, 85, 82, 86, 108, 135, 112, 119, 6, 89, 88, 5, 42, 176, 0, 48, 7, 157, 105, 81, 12, 120, 140, 9, 2, 164, 162, 77, 158, 139, 152, 155, 150, 13, 3, 163, 151, 153, 159, 147, 161, 4, 136, 87, 172, 173, 142, 144, 146, 145, 169, 138, 8, 171, 179, 177, 121, 110, 148, 10, 174, 178, 143, 141, 154, 137, 167, 168, 170, 165, and 166.

FIG. 263 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 10/15.

According to the original GW pattern (B) of FIG. 263, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 16, 163, 92, 56, 111, 141, 65, 118, 78, 55, 5, 148, 19, 153, 75, 128, 32, 178, 22, 156, 99, 124, 4, 168, 20, 115, 87, 122, 9, 166, 27, 155, 94, 134, 38, 137, 67, 161, 90, 127, 43, 171, 64, 162, 98, 133, 34, 138, 73, 154, 100, 58, 103, 169, 23, 117, 88, 50, 13, 175, 68, 39, 102, 54, 37, 149, 29, 150, 104, 59, 3, 139, 69, 110, 77, 131, 42, 142, 25, 158, 80, 47, 35, 143, 72, 151, 84, 57, 8, 176, 61, 46, 41, 51, 10, 173, 63, 107, 125, 48, 11, 177, 24, 30, 91, 76, 109, 140, 74, 114, 82, 120, 1, 79, 66, 119, 93, 159, 36, 174, 26, 112, 101, 123, 44, 145, 60, 157, 97, 45, 33, 167, 70, 152, 85, 126, 40, 135, 62, 108, 95, 49, 31, 147, 71, 113, 89, 132, 6, 144, 18, 105, 83, 130, 2, 172, 17, 164, 81, 52, 7, 179, 28, 160, 136, 121, 14, 146, 15, 106, 86, 129, 12, 170, 21, 116, 96, 53, 0, and 165.

According to the converted GW pattern (A) of FIG. 263, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 16, 65, 19, 22, 20, 27, 67, 64, 73, 23, 68, 29, 69, 25, 72, 61, 63, 24, 74, 66, 26, 60, 70, 62, 71, 18, 17, 28, 15, 21, 163, 118, 153, 156, 115, 155, 161, 162, 154, 117, 39, 150, 110, 158, 151, 46, 107, 30, 114, 119, 112, 157, 152, 108, 113, 105, 164, 160, 106, 116, 92, 78, 75, 99, 87, 94, 90, 98, 100, 88, 102, 104, 77, 80, 84, 41, 125, 91, 82, 93, 101, 97, 85, 95, 89, 83, 81, 136, 86, 96, 56, 55, 128, 124, 122, 134, 127, 133, 58, 50, 54, 59, 131, 47, 57, 51, 48, 76, 120, 159, 123, 45, 126, 49, 132, 130, 52, 121, 129, 53, 111, 5, 32, 4, 9, 38, 43, 34, 103, 13, 37, 3, 42, 35, 8, 10, 11, 109, 1, 36, 44, 33, 40, 31, 6, 2, 7, 14, 12, 0, 141, 148, 178, 168, 166, 137, 171, 138, 169, 175, 149, 139, 142, 143, 176, 173, 177, 140, 79, 174, 145, 167, 135, 147, 144, 172, 179, 146, 170, and 165.

FIG. 264 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 11/15.

According to the original GW pattern (A) of FIG. 264, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72, 116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9, 5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55, 103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28, 104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125, 58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101, 94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135, 141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47, 80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148, 154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42, 114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161, 167, 173, and 179.

According to the converted GW pattern (B) of FIG. 264, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 12, 0, 10, 4, 3, 21, 15, 14, 22, 19, 20, 18, 2, 9, 13, 6, 7, 1, 16, 5, 11, 8, 17, 26, 27, 23, 28, 24, 25, 29, 50, 66, 104, 44, 87, 39, 35, 68, 37, 101, 41, 73, 74, 52, 57, 94, 120, 121, 38, 96, 115, 118, 47, 105, 70, 117, 46, 130, 80, 77, 108, 84, 65, 69, 59, 42, 32, 128, 129, 71, 62, 114, 112, 100, 107, 83, 88, 93, 54, 63, 75, 34, 45, 82, 30, 60, 119, 86, 56, 111, 122, 127, 110, 124, 131, 109, 72, 81, 31, 48, 61, 67, 116, 99, 43, 106, 126, 79, 36, 53, 97, 89, 113, 123, 90, 55, 78, 40, 92, 64, 49, 103, 125, 102, 51, 76, 85, 95, 58, 91, 98, 33, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, and 179.

FIG. 265 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 265, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 83, 93, 94, 47, 55, 40, 38, 77, 110, 124, 87, 61, 102, 76, 33, 35, 92, 59, 74, 11, 138, 72, 67, 37, 10, 95, 139, 131, 44, 57, 97, 53, 142, 0, 136, 9, 143, 86, 100, 21, 15, 75, 62, 19, 65, 129, 101, 79, 22, 68, 73, 23, 18, 81, 98, 112, 8, 128, 103, 25, 43, 126, 54, 90, 28, 109, 46, 91, 41, 82, 113, 134, 52, 105, 78, 27, 135, 96, 56, 140, 64, 66, 89, 34, 120, 108, 63, 45, 69, 121, 88, 39, 29, 133, 106, 117, 127, 32, 42, 58, 71, 118, 51, 84, 85, 80, 104, 132, 111, 30, 26, 48, 50, 31, 141, 116, 123, 114, 70, 107, 178, 145, 173, 36, 144, 130, 176, 171, 175, 125, 99, 162, 159, 20, 164, 115, 169, 172, 165, 161, 151, 119, 122, 152, 157, 4, 137, 148, 153, 170, 154, 166, 13, 150, 16, 167, 174, 163, 49, 6, 168, 147, 146, 1, 149, 158, 179, 12, 5, 160, 177, 60, 24, 156, 7, 155, 17, 3, 2, and 14.

According to the converted GW pattern (B) of FIG. 265, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 83, 97, 43, 88, 178, 154, 93, 53, 126, 39, 145, 166, 94, 142, 54, 29, 173, 13, 47, 0, 90, 133, 36, 150, 55, 136, 28, 106, 144, 16, 40, 9, 109, 117, 130, 167, 38, 143, 46, 127, 176, 174, 77, 86, 91, 32, 171, 163, 110, 100, 41, 42, 175, 49, 124, 21, 82, 58, 125, 6, 87, 15, 113, 71, 99, 168, 61, 75, 134, 118, 162, 147, 102, 62, 52, 51, 159, 146, 76, 19, 105, 84, 20, 1, 33, 65, 78, 85, 164, 149, 35, 129, 27, 80, 115, 158, 92, 101, 135, 104, 169, 179, 59, 79, 96, 132, 172, 12, 74, 22, 56, 111, 165, 5, 11, 68, 140, 30, 161, 160, 138, 73, 64, 26, 151, 177, 72, 23, 66, 48, 119, 60, 67, 18, 89, 50, 122, 24, 37, 81, 34, 31, 152, 156, 10, 98, 120, 141, 157, 7, 95, 112, 108, 116, 4, 155, 139, 8, 63, 123, 137, 17, 131, 128, 45, 114, 148, 3, 44, 103, 69, 70, 153, 2, 57, 25, 121, 107, 170, and 14.

FIG. 266 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM and the code rate r is 13/15.

According to the original GW pattern (B) of FIG. 266, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 146, 91, 63, 144, 46, 12, 58, 137, 25, 79, 70, 33, 134, 148, 66, 38, 163, 118, 139, 130, 72, 92, 160, 23, 133, 153, 128, 86, 152, 106, 53, 93, 61, 5, 158, 172, 121, 135, 44, 149, 168, 0, 124, 143, 27, 30, 151, 114, 113, 43, 138, 89, 159, 17, 120, 136, 102, 81, 170, 176, 142, 104, 21, 78, 155, 8, 52, 95, 62, 40, 174, 6, 131, 48, 18, 1, 179, 34, 123, 77, 26, 84, 157, 85, 56, 147, 67, 76, 162, 10, 51, 103, 140, 87, 175, 115, 4, 101, 69, 80, 169, 75, 49, 97, 154, 83, 14, 2, 132, 96, 16, 37, 166, 109, 54, 42, 28, 32, 171, 119, 55, 94, 65, 20, 165, 3, 47, 90, 117, 88, 177, 11, 59, 68, 73, 41, 150, 111, 127, 100, 110, 31, 167, 13, 122, 145, 71, 22, 173, 116, 126, 141, 29, 39, 178, 57, 125, 36, 19, 7, 156, 107, 9, 98, 74, 45, 161, 112, 50, 99, 24, 35, 164, 64, 129, 15, 60, 82, 108, and 105.

According to the converted GW pattern (A) of FIG. 266, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 146, 58, 134, 139, 133, 53, 121, 124, 113, 120, 142, 52, 131, 123, 56, 51, 4, 49, 132, 54, 55, 47, 59, 127, 122, 126, 125, 9, 50, 129, 91, 137, 148, 130, 153, 93, 135, 143, 43, 136, 104, 95, 48, 77, 147, 103, 101, 97, 96, 42, 94, 90, 68, 100, 145, 141, 36, 98, 99, 15, 63, 25, 66, 72, 128, 61, 44, 27, 138, 102, 21, 62, 18, 26, 67, 140, 69, 154, 16, 28, 65, 117, 73, 110, 71, 29, 19, 74, 24, 60, 144, 79, 38, 92, 86, 5, 149, 30, 89, 81, 78, 40, 1, 84, 76, 87, 80, 83, 37, 32, 20, 88, 41, 31, 22, 39, 7, 45, 35, 82, 46, 70, 163, 160, 152, 158, 168, 151, 159, 170, 155, 174, 179, 157, 162, 175, 169, 14, 166, 171, 165, 177, 150, 167, 173, 178, 156, 161, 164, 108, 12, 33, 118, 23, 106, 172, 0, 114, 17, 176, 8, 6, 34, 85, 10, 115, 75, 2, 109, 119, 3, 11, 111, 13, 116, 57, 107, 112, 64, and 105.

FIG. 267 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 267, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 112, 78, 104, 6, 59, 80, 49, 120, 114, 27, 113, 3, 109, 44, 69, 164, 91, 137, 39, 31, 21, 127, 151, 8, 47, 176, 117, 68, 122, 148, 79, 73, 7, 166, 51, 50, 116, 66, 152, 61, 29, 107, 22, 154, 118, 94, 24, 35, 55, 38, 88, 54, 2, 15, 19, 67, 101, 74, 169, 138, 41, 162, 175, 136, 62, 161, 121, 163, 115, 135, 123, 25, 140, 156, 58, 33, 119, 111, 146, 129, 150, 147, 97, 18, 60, 4, 81, 168, 43, 105, 36, 65, 13, 5, 108, 145, 23, 70, 20, 173, 159, 100, 128, 172, 170, 1, 37, 83, 102, 103, 157, 139, 179, 32, 144, 92, 131, 75, 155, 14, 9, 149, 63, 11, 134, 53, 99, 17, 57, 90, 30, 98, 64, 40, 87, 158, 77, 93, 124, 46, 171, 141, 133, 85, 177, 132, 26, 160, 42, 34, 82, 96, 48, 10, 142, 125, 178, 153, 72, 45, 89, 52, 28, 126, 143, 167, 76, 86, 130, 110, 174, 16, 165, 56, 84, 95, 0, 106, 12, and 71.

According to the converted GW pattern (B) of FIG. 267, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 112, 151, 118, 121, 43, 157, 64, 142, 78, 8, 94, 163, 105, 139, 40, 125, 104, 47, 24, 115, 36, 179, 87, 178, 6, 176, 35, 135, 65, 32, 158, 153, 59, 117, 55, 123, 13, 144, 77, 72, 80, 68, 38, 25, 5, 92, 93, 45, 49, 122, 88, 140, 108, 131, 124, 89, 120, 148, 54, 156, 145, 75, 46, 52, 114, 79, 2, 58, 23, 155, 171, 28, 27, 73, 15, 33, 70, 14, 141, 126, 113, 7, 19, 119, 20, 9, 133, 143, 3, 166, 67, 111, 173, 149, 85, 167, 109, 51, 101, 146, 159, 63, 177, 76, 44, 50, 74, 129, 100, 11, 132, 86, 69, 116, 169, 150, 128, 134, 26, 130, 164, 66, 138, 147, 172, 53, 160, 110, 91, 152, 41, 97, 170, 99, 42, 174, 137, 61, 162, 18, 1, 17, 34, 16, 39, 29, 175, 60, 37, 57, 82, 165, 31, 107, 136, 4, 83, 90, 96, 56, 21, 22, 62, 81, 102, 30, 48, 84, 127, 154, 161, 168, 103, 98, 10, 95, 0, 106, 12, and 71.

FIG. 268 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 268, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 136, 28, 85, 38, 40, 89, 133, 117, 3, 58, 154, 77, 14, 179, 96, 101, 26, 169, 37, 83, 162, 165, 24, 66, 109, 126, 10, 155, 70, 157, 105, 175, 67, 158, 32, 42, 147, 140, 30, 7, 92, 59, 119, 56, 0, 5, 90, 174, 13, 47, 76, 88, 86, 108, 27, 18, 12, 8, 61, 145, 75, 125, 112, 69, 120, 137, 116, 20, 178, 98, 176, 29, 68, 168, 124, 21, 35, 150, 131, 159, 163, 84, 23, 123, 65, 103, 93, 99, 102, 31, 64, 74, 46, 94, 80, 129, 142, 128, 148, 111, 134, 173, 60, 118, 2, 170, 135, 1, 115, 143, 95, 177, 73, 43, 11, 114, 91, 78, 107, 172, 25, 36, 164, 149, 153, 110, 44, 146, 82, 127, 45, 33, 50, 41, 52, 156, 34, 4, 79, 141, 138, 122, 53, 160, 81, 16, 100, 130, 71, 121, 132, 9, 22, 113, 6, 152, 15, 171, 17, 57, 49, 151, 161, 63, 55, 139, 166, 97, 19, 51, 72, 167, 106, 48, 144, 87, 104, 62, 54, and 39.

According to the converted GW pattern (B) of FIG. 268, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 136, 24, 0, 116, 102, 95, 50, 6, 28, 66, 5, 20, 31, 177, 41, 152, 85, 109, 90, 178, 64, 73, 52, 15, 38, 126, 174, 98, 74, 43, 156, 171, 40, 10, 13, 176, 46, 11, 34, 17, 89, 155, 47, 29, 94, 114, 4, 57, 133, 70, 76, 68, 80, 91, 79, 49, 117, 157, 88, 168, 129, 78, 141, 151, 3, 105, 86, 124, 142, 107, 138, 161, 58, 175, 108, 21, 128, 172, 122, 63, 154, 67, 27, 35, 148, 25, 53, 55, 77, 158, 18, 150, 111, 36, 160, 139, 14, 32, 12, 131, 134, 164, 81, 166, 179, 42, 8, 159, 173, 149, 16, 97, 96, 147, 61, 163, 60, 153, 100, 19, 101, 140, 145, 84, 118, 110, 130, 51, 26, 30, 75, 23, 2, 44, 71, 72, 169, 7, 125, 123, 170, 146, 121, 167, 37, 92, 112, 65, 135, 82, 132, 106, 83, 59, 69, 103, 1, 127, 9, 48, 162, 119, 120, 93, 115, 45, 22, 144, 165, 56, 137, 99, 143, 33, 113, 87, 104, 62, 54, and 39.

FIG. 269 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 269, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 13, 121, 137, 29, 27, 1, 70, 116, 35, 132, 109, 51, 55, 58, 11, 67, 136, 25, 145, 7, 75, 107, 45, 21, 127, 52, 90, 22, 100, 123, 69, 112, 155, 92, 151, 59, 5, 179, 44, 87, 56, 139, 65, 170, 46, 0, 124, 78, 166, 8, 61, 97, 120, 103, 4, 19, 64, 79, 28, 134, 93, 86, 60, 135, 126, 53, 63, 14, 122, 17, 150, 76, 42, 39, 23, 153, 95, 66, 50, 141, 176, 34, 161, 26, 106, 10, 43, 85, 131, 2, 147, 148, 144, 54, 115, 146, 101, 172, 114, 119, 3, 96, 133, 99, 167, 164, 9, 142, 68, 149, 94, 83, 16, 175, 73, 38, 143, 159, 130, 84, 169, 18, 138, 102, 72, 47, 32, 160, 82, 81, 168, 30, 12, 173, 156, 158, 125, 98, 62, 178, 48, 163, 117, 110, 91, 37, 80, 105, 31, 174, 111, 49, 113, 108, 74, 157, 128, 24, 118, 40, 88, 177, 154, 6, 162, 129, 77, 36, 165, 20, 89, 140, 15, 33, 104, 152, 71, 171, 57, and 41.

According to the converted GW pattern (B) of FIG. 269, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 13, 45, 46, 63, 131, 94, 12, 74, 121, 21, 0, 14, 2, 83, 173, 157, 137, 127, 124, 122, 147, 16, 156, 128, 29, 52, 78, 17, 148, 175, 158, 24, 27, 90, 166, 150, 144, 73, 125, 118, 1, 22, 8, 76, 54, 38, 98, 40, 70, 100, 61, 42, 115, 143, 62, 88, 116, 123, 97, 39, 146, 159, 178, 177, 35, 69, 120, 23, 101, 130, 48, 154, 132, 112, 103, 153, 172, 84, 163, 6, 109, 155, 4, 95, 114, 169, 117, 162, 51, 92, 19, 66, 119, 18, 110, 129, 55, 151, 64, 50, 3, 138, 91, 77, 58, 59, 79, 141, 96, 102, 37, 36, 11, 5, 28, 176, 133, 72, 80, 165, 67, 179, 134, 34, 99, 47, 105, 20, 136, 44, 93, 161, 167, 32, 31, 89, 25, 87, 86, 26, 164, 160, 174, 140, 145, 56, 60, 106, 9, 82, 111, 15, 7, 139, 135, 10, 142, 81, 49, 33, 75, 65, 126, 43, 68, 168, 113, 104, 107, 170, 53, 85, 149, 30, 108, 152, 71, 171, 57, and 41.

FIG. 270 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 5/15.

According to the original GW pattern (B) of FIG. 270, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 39, 45, 128, 84, 143, 148, 2, 75, 43, 50, 130, 87, 137, 151, 7, 71, 55, 51, 133, 90, 140, 149, 6, 177, 37, 124, 99, 83, 23, 159, 0, 176, 41, 121, 96, 89, 30, 161, 18, 172, 60, 49, 134, 104, 139, 166, 14, 179, 62, 48, 129, 105, 146, 160, 16, 174, 33, 54, 132, 112, 145, 150, 9, 77, 34, 117, 92, 82, 136, 165, 4, 67, 36, 44, 101, 81, 141, 156, 3, 175, 58, 47, 91, 102, 32, 158, 13, 178, 63, 118, 100, 85, 26, 167, 1, 173, 38, 116, 131, 107, 138, 162, 8, 72, 42, 115, 98, 108, 24, 152, 17, 171, 64, 123, 94, 110, 28, 147, 19, 169, 61, 46, 97, 106, 144, 164, 5, 70, 59, 53, 127, 88, 31, 153, 10, 73, 66, 119, 126, 111, 29, 155, 15, 170, 57, 120, 125, 80, 142, 168, 11, 68, 56, 52, 95, 103, 27, 154, 21, 78, 40, 122, 93, 86, 25, 163, 20, 79, 35, 114, 135, 109, 22, 157, 12, 69, 65, 74, 76, and 113.

According to the converted GW pattern (A) of FIG. 270, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 39, 43, 55, 37, 41, 60, 62, 33, 34, 36, 58, 63, 38, 42, 64, 61, 59, 66, 57, 56, 40, 35, 45, 50, 51, 124, 121, 49, 48, 54, 117, 44, 47, 118, 116, 115, 123, 46, 53, 119, 120, 52, 122, 114, 128, 130, 133, 99, 96, 134, 129, 132, 92, 101, 91, 100, 131, 98, 94, 97, 127, 126, 125, 95, 93, 135, 84, 87, 90, 83, 89, 104, 105, 112, 82, 81, 102, 85, 107, 108, 110, 106, 88, 111, 80, 103, 86, 109, 143, 137, 140, 23, 30, 139, 146, 145, 136, 141, 32, 26, 138, 24, 28, 144, 31, 29, 142, 27, 25, 22, 148, 151, 149, 159, 161, 166, 160, 150, 165, 156, 158, 167, 162, 152, 147, 164, 153, 155, 168, 154, 163, 157, 2, 7, 6, 0, 18, 14, 16, 9, 4, 3, 13, 1, 8, 17, 19, 5, 10, 15, 11, 21, 20, 12, 75, 71, 177, 176, 172, 179, 174, 77, 67, 175, 178, 173, 72, 171, 169, 70, 73, 170, 68, 78, 79, 69, 65, 74, 76, and 113.

FIG. 271 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 6/15.

According to the original GW pattern (B) of FIG. 271, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 99, 100, 15, 107, 54, 76, 153, 174, 61, 0, 36, 71, 62, 137, 108, 114, 65, 98, 151, 19, 112, 109, 152, 117, 35, 93, 43, 90, 154, 73, 150, 165, 23, 16, 91, 5, 169, 175, 120, 149, 26, 59, 49, 56, 156, 136, 110, 80, 58, 55, 40, 103, 159, 83, 127, 111, 155, 167, 11, 52, 116, 142, 133, 1, 2, 96, 77, 86, 122, 6, 131, 29, 51, 21, 17, 45, 126, 12, 3, 168, 41, 30, 37, 64, 164, 78, 8, 118, 113, 39, 48, 140, 14, 60, 82, 134, 25, 33, 50, 84, 28, 105, 123, 145, 7, 27, 34, 92, 115, 147, 74, 10, 68, 102, 67, 63, 101, 18, 66, 129, 24, 4, 119, 87, 42, 170, 143, 121, 38, 57, 95, 148, 89, 81, 158, 171, 32, 22, 69, 53, 130, 104, 161, 75, 141, 9, 47, 79, 162, 146, 124, 157, 70, 106, 31, 132, 166, 128, 138, 125, 44, 13, 85, 88, 135, 144, 173, 163, 20, 46, 97, 94, 139, 172, 72, 160, 176, 177, 178, and 179.

According to the converted GW pattern (A) of FIG. 271, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 99, 61, 65, 35, 23, 26, 58, 155, 2, 51, 41, 113, 25, 7, 68, 24, 38, 32, 141, 70, 44, 20, 100, 0, 98, 93, 16, 59, 55, 167, 96, 21, 30, 39, 33, 27, 102, 4, 57, 22, 9, 106, 13, 46, 15, 36, 151, 43, 91, 49, 40, 11, 77, 17, 37, 48, 50, 34, 67, 119, 95, 69, 47, 31, 85, 97, 107, 71, 19, 90, 5, 56, 103, 52, 86, 45, 64, 140, 84, 92, 63, 87, 148, 53, 79, 132, 88, 94, 54, 62, 112, 154, 169, 156, 159, 116, 122, 126, 164, 14, 28, 115, 101, 42, 89, 130, 162, 166, 135, 139, 76, 137, 109, 73, 175, 136, 83, 142, 6, 12, 78, 60, 105, 147, 18, 170, 81, 104, 146, 128, 144, 172, 153, 108, 152, 150, 120, 110, 127, 133, 131, 3, 8, 82, 123, 74, 66, 143, 158, 161, 124, 138, 173, 72, 174, 114, 117, 165, 149, 80, 111, 1, 29, 168, 118, 134, 145, 10, 129, 121, 171, 75, 157, 125, 163, 160, 176, 177, 178, and 179.

FIG. 272 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 272, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 24, 157, 0, 43, 126, 172, 135, 65, 32, 18, 114, 42, 162, 67, 104, 61, 23, 11, 4, 96, 163, 75, 109, 58, 79, 154, 3, 95, 168, 73, 103, 60, 84, 148, 113, 40, 164, 173, 143, 49, 29, 156, 7, 89, 132, 179, 138, 53, 85, 12, 117, 36, 122, 66, 107, 64, 28, 147, 2, 90, 131, 70, 144, 55, 26, 15, 112, 35, 128, 176, 106, 59, 80, 19, 6, 92, 129, 174, 99, 62, 82, 13, 121, 41, 127, 71, 139, 63, 25, 151, 9, 39, 159, 69, 142, 52, 77, 21, 119, 38, 167, 178, 101, 56, 87, 155, 5, 91, 166, 169, 146, 50, 81, 20, 111, 88, 165, 177, 108, 47, 27, 149, 115, 33, 161, 72, 102, 57, 86, 16, 110, 97, 123, 68, 100, 48, 31, 14, 8, 93, 130, 170, 133, 44, 78, 150, 118, 94, 158, 76, 134, 46, 83, 152, 1, 37, 160, 171, 136, 54, 22, 17, 116, 34, 125, 175, 105, 45, 30, 153, 10, 98, 124, 74, 137, 51, 120, 141, 140, and 145.

According to the converted GW pattern (A) of FIG. 272, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 24, 32, 23, 79, 84, 29, 85, 28, 26, 80, 82, 25, 77, 87, 81, 27, 86, 31, 78, 83, 22, 30, 157, 18, 11, 154, 148, 156, 12, 147, 15, 19, 13, 151, 21, 155, 20, 149, 16, 14, 150, 152, 17, 153, 0, 114, 4, 3, 113, 7, 117, 2, 112, 6, 121, 9, 119, 5, 111, 115, 110, 8, 118, 1, 116, 10, 43, 42, 96, 95, 40, 89, 36, 90, 35, 92, 41, 39, 38, 91, 88, 33, 97, 93, 94, 37, 34, 98, 126, 162, 163, 168, 164, 132, 122, 131, 128, 129, 127, 159, 167, 166, 165, 161, 123, 130, 158, 160, 125, 124, 172, 67, 75, 73, 173, 179, 66, 70, 176, 174, 71, 69, 178, 169, 177, 72, 68, 170, 76, 171, 175, 74, 135, 104, 109, 103, 143, 138, 107, 144, 106, 99, 139, 142, 101, 146, 108, 102, 100, 133, 134, 136, 105, 137, 65, 61, 58, 60, 49, 53, 64, 55, 59, 62, 63, 52, 56, 50, 47, 57, 48, 44, 46, 54, 45, 51, 120, 141, 140, and 145.

FIG. 273 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 8/15.

According to the original GW pattern (B) of FIG. 273, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 85, 3, 148, 161, 96, 99, 154, 13, 78, 160, 61, 36, 21, 141, 121, 115, 82, 1, 59, 72, 43, 135, 168, 139, 46, 10, 56, 67, 108, 134, 111, 105, 66, 89, 137, 130, 104, 143, 113, 11, 84, 157, 32, 73, 90, 38, 117, 146, 53, 2, 60, 93, 91, 71, 114, 19, 47, 4, 26, 75, 109, 41, 50, 153, 54, 163, 31, 24, 106, 42, 170, 62, 80, 164, 65, 128, 12, 142, 167, 155, 88, 8, 22, 131, 158, 33, 178, 145, 70, 9, 51, 69, 102, 140, 173, 147, 83, 165, 30, 126, 100, 138, 171, 103, 45, 159, 27, 74, 97, 122, 120, 16, 52, 162, 132, 124, 94, 133, 172, 149, 86, 77, 25, 68, 177, 64, 174, 15, 0, 125, 63, 35, 34, 40, 179, 20, 44, 7, 55, 28, 101, 150, 110, 18, 119, 5, 29, 76, 107, 136, 112, 144, 48, 81, 57, 49, 92, 95, 118, 17, 156, 166, 23, 129, 79, 37, 175, 152, 87, 6, 58, 127, 98, 123, 39, 14, 116, 169, 176, and 151.

According to the converted GW pattern (A) of FIG. 273, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 85, 78, 82, 46, 66, 84, 53, 47, 54, 80, 88, 70, 83, 45, 52, 86, 0, 44, 119, 48, 156, 87, 3, 160, 1, 10, 89, 157, 2, 4, 163, 164, 8, 9, 165, 159, 162, 77, 125, 7, 5, 81, 166, 6, 148, 61, 59, 56, 137, 32, 60, 26, 31, 65, 22, 51, 30, 27, 132, 25, 63, 55, 29, 57, 23, 58, 161, 36, 72, 67, 130, 73, 93, 75, 24, 128, 131, 69, 126, 74, 124, 68, 35, 28, 76, 49, 129, 127, 96, 21, 43, 108, 104, 90, 91, 109, 106, 12, 158, 102, 100, 97, 94, 177, 34, 101, 107, 92, 79, 98, 99, 141, 135, 134, 143, 38, 71, 41, 42, 142, 33, 140, 138, 122, 133, 64, 40, 150, 136, 95, 37, 123, 154, 121, 168, 111, 113, 117, 114, 50, 170, 167, 178, 173, 171, 120, 172, 174, 179, 110, 112, 118, 175, 39, 13, 115, 139, 105, 11, 146, 19, 153, 62, 155, 145, 147, 103, 16, 149, 15, 20, 18, 144, 17, 152, 14, 116, 169, 176, and 151.

FIG. 274 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 9/15.

According to the original GW pattern (A) of FIG. 274, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 58, 70, 23, 32, 26, 63, 55, 48, 35, 41, 53, 20, 38, 51, 61, 65, 44, 29, 7, 2, 113, 68, 96, 104, 106, 89, 27, 0, 119, 21, 4, 49, 46, 100, 13, 36, 57, 98, 102, 9, 42, 39, 33, 62, 22, 95, 101, 15, 91, 25, 93, 132, 69, 87, 47, 59, 67, 124, 17, 11, 31, 43, 40, 37, 85, 50, 97, 140, 45, 92, 56, 30, 34, 60, 107, 24, 52, 94, 64, 5, 71, 90, 66, 103, 88, 86, 84, 19, 169, 159, 147, 126, 28, 130, 14, 162, 144, 166, 108, 153, 115, 135, 120, 122, 112, 139, 151, 156, 16, 172, 164, 123, 99, 54, 136, 81, 105, 128, 116, 150, 155, 76, 18, 142, 170, 175, 83, 146, 78, 109, 73, 131, 127, 82, 167, 77, 110, 79, 137, 152, 3, 173, 148, 72, 158, 117, 1, 6, 12, 8, 161, 74, 143, 133, 168, 171, 134, 163, 138, 121, 141, 160, 111, 10, 149, 80, 75, 165, 157, 174, 129, 145, 114, 125, 154, 118, 176, 177, 178, and 179.

According to the converted GW pattern (B) of FIG. 274, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 58, 96, 22, 97, 169, 164, 127, 168, 70, 104, 95, 140, 159, 123, 82, 171, 23, 106, 101, 45, 147, 99, 167, 134, 32, 89, 15, 92, 126, 54, 77, 163, 26, 27, 91, 56, 28, 136, 110, 138, 63, 0, 25, 30, 130, 81, 79, 121, 55, 119, 93, 34, 14, 105, 137, 141, 48, 21, 132, 60, 162, 128, 152, 160, 35, 4, 69, 107, 144, 116, 3, 111, 41, 49, 87, 24, 166, 150, 173, 10, 53, 46, 47, 52, 108, 155, 148, 149, 20, 100, 59, 94, 153, 76, 72, 80, 38, 13, 67, 64, 115, 18, 158, 75, 51, 36, 124, 5, 135, 142, 117, 165, 61, 57, 17, 71, 120, 170, 1, 157, 65, 98, 11, 90, 122, 175, 6, 174, 44, 102, 31, 66, 112, 83, 12, 129, 29, 9, 43, 103, 139, 146, 8, 145, 7, 42, 40, 88, 151, 78, 161, 114, 2, 39, 37, 86, 156, 109, 74, 125, 113, 33, 85, 84, 16, 73, 143, 154, 68, 62, 50, 19, 172, 131, 133, 118, 176, 177, 178, and 179.

FIG. 275 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 10/15.

According to the original GW pattern (B) of FIG. 275, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 45, 31, 67, 35, 159, 157, 177, 2, 44, 23, 73, 148, 163, 118, 176, 4, 14, 97, 142, 37, 143, 149, 179, 3, 12, 32, 140, 42, 167, 166, 41, 126, 13, 30, 144, 57, 113, 147, 173, 6, 52, 24, 39, 64, 80, 112, 104, 174, 11, 151, 71, 109, 162, 79, 171, 127, 46, 92, 38, 132, 81, 120, 100, 1, 53, 88, 76, 60, 103, 139, 99, 125, 48, 93, 135, 161, 77, 110, 107, 121, 18, 95, 69, 63, 83, 111, 170, 7, 16, 98, 141, 61, 86, 116, 172, 130, 49, 25, 40, 65, 87, 108, 101, 5, 21, 89, 75, 43, 82, 146, 105, 128, 17, 29, 106, 34, 160, 155, 175, 124, 15, 28, 134, 62, 119, 145, 72, 10, 58, 91, 74, 36, 68, 150, 8, 9, 54, 26, 137, 56, 165, 115, 114, 0, 47, 27, 22, 20, 168, 154, 102, 123, 50, 94, 66, 33, 85, 59, 164, 131, 51, 90, 70, 138, 84, 117, 178, 122, 19, 96, 156, 55, 78, 158, 169, 129, 133, 152, 136, and 153.

According to the converted GW pattern (A) of FIG. 275, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 45, 44, 14, 12, 13, 52, 11, 46, 53, 48, 18, 16, 49, 21, 17, 15, 58, 54, 47, 50, 51, 19, 31, 23, 97, 32, 30, 24, 151, 92, 88, 93, 95, 98, 25, 89, 29, 28, 91, 26, 27, 94, 90, 96, 67, 73, 142, 140, 144, 39, 71, 38, 76, 135, 69, 141, 40, 75, 106, 134, 74, 137, 22, 66, 70, 156, 35, 148, 37, 42, 57, 64, 109, 132, 60, 161, 63, 61, 65, 43, 34, 62, 36, 56, 20, 33, 138, 55, 159, 163, 143, 167, 113, 80, 162, 81, 103, 77, 83, 86, 87, 82, 160, 119, 68, 165, 168, 85, 84, 78, 157, 118, 149, 166, 147, 112, 79, 120, 139, 110, 111, 116, 108, 146, 155, 145, 150, 115, 154, 59, 117, 158, 177, 176, 179, 41, 173, 104, 171, 100, 99, 107, 170, 172, 101, 105, 175, 72, 8, 114, 102, 164, 178, 169, 2, 4, 3, 126, 6, 174, 127, 1, 125, 121, 7, 130, 5, 128, 124, 10, 9, 0, 123, 131, 122, 129, 133, 152, 136, and 153.

FIG. 276 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 11/15.

According to the original GW pattern (B) of FIG. 276, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 27, 68, 35, 117, 138, 83, 127, 10, 60, 73, 47, 115, 155, 81, 170, 9, 65, 66, 52, 112, 150, 77, 171, 161, 22, 20, 39, 106, 147, 90, 126, 165, 23, 16, 45, 113, 154, 86, 173, 158, 24, 71, 40, 107, 136, 94, 128, 163, 31, 72, 33, 101, 134, 80, 175, 7, 61, 19, 49, 111, 135, 92, 130, 6, 62, 74, 43, 116, 133, 89, 129, 8, 28, 15, 34, 105, 146, 84, 174, 4, 32, 75, 44, 118, 132, 96, 169, 159, 58, 18, 42, 100, 141, 87, 131, 157, 63, 11, 48, 108, 151, 79, 177, 168, 26, 17, 36, 102, 137, 95, 122, 1, 25, 21, 50, 120, 153, 97, 121, 0, 55, 14, 46, 114, 152, 91, 178, 3, 30, 13, 37, 103, 145, 82, 125, 166, 57, 76, 51, 99, 144, 85, 123, 162, 56, 12, 53, 119, 139, 78, 179, 5, 64, 70, 54, 110, 148, 93, 172, 164, 29, 69, 38, 109, 143, 88, 124, 160, 59, 67, 41, 104, 149, 98, 176, 2, 167, 156, 140, and 142.

According to the converted GW pattern (A) of FIG. 276, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 27, 60, 65, 22, 23, 24, 31, 61, 62, 28, 32, 58, 63, 26, 25, 55, 30, 57, 56, 64, 29, 59, 68, 73, 66, 20, 16, 71, 72, 19, 74, 15, 75, 18, 11, 17, 21, 14, 13, 76, 12, 70, 69, 67, 35, 47, 52, 39, 45, 40, 33, 49, 43, 34, 44, 42, 48, 36, 50, 46, 37, 51, 53, 54, 38, 41, 117, 115, 112, 106, 113, 107, 101, 111, 116, 105, 118, 100, 108, 102, 120, 114, 103, 99, 119, 110, 109, 104, 138, 155, 150, 147, 154, 136, 134, 135, 133, 146, 132, 141, 151, 137, 153, 152, 145, 144, 139, 148, 143, 149, 83, 81, 77, 90, 86, 94, 80, 92, 89, 84, 96, 87, 79, 95, 97, 91, 82, 85, 78, 93, 88, 98, 127, 170, 171, 126, 173, 128, 175, 130, 129, 174, 169, 131, 177, 122, 121, 178, 125, 123, 179, 172, 124, 176, 10, 9, 161, 165, 158, 163, 7, 6, 8, 4, 159, 157, 168, 1, 0, 3, 166, 162, 5, 164, 160, 2, 167, 156, 140, and 142.

FIG. 277 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 277, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 51, 122, 91, 111, 95, 100, 119, 130, 78, 57, 65, 26, 61, 126, 105, 143, 70, 132, 39, 102, 115, 116, 6, 14, 3, 21, 71, 134, 2, 0, 140, 106, 7, 118, 23, 35, 20, 17, 50, 48, 112, 13, 66, 5, 75, 42, 129, 107, 30, 45, 137, 114, 37, 87, 53, 85, 101, 141, 120, 99, 88, 117, 64, 28, 135, 138, 108, 113, 58, 97, 38, 124, 86, 33, 74, 32, 29, 128, 67, 104, 80, 127, 56, 34, 89, 94, 49, 55, 93, 136, 68, 62, 54, 40, 81, 103, 121, 76, 44, 84, 96, 123, 154, 98, 82, 142, 46, 169, 131, 72, 47, 69, 125, 31, 83, 36, 59, 90, 79, 52, 133, 60, 92, 139, 110, 27, 73, 43, 77, 109, 63, 41, 168, 147, 161, 165, 175, 162, 164, 158, 157, 160, 150, 171, 167, 145, 151, 153, 9, 155, 170, 146, 166, 149, 15, 159, 11, 176, 152, 156, 144, 148, 172, 178, 24, 22, 179, 4, 163, 174, 173, 19, 10, 177, 12, 16, 1, 8, 18, and 25.

According to the converted GW pattern (B) of FIG. 277, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 51, 6, 75, 108, 93, 47, 168, 15, 122, 14, 42, 113, 136, 69, 147, 159, 91, 3, 129, 58, 68, 125, 161, 11, 111, 21, 107, 97, 62, 31, 165, 176, 95, 71, 30, 38, 54, 83, 175, 152, 100, 134, 45, 124, 40, 36, 162, 156, 119, 2, 137, 86, 81, 59, 164, 144, 130, 0, 114, 33, 103, 90, 158, 148, 78, 140, 37, 74, 121, 79, 157, 172, 57, 106, 87, 32, 76, 52, 160, 178, 65, 7, 53, 29, 44, 133, 150, 24, 26, 118, 85, 128, 84, 60, 171, 22, 61, 23, 101, 67, 96, 92, 167, 179, 126, 35, 141, 104, 123, 139, 145, 4, 105, 20, 120, 80, 154, 110, 151, 163, 143, 17, 99, 127, 98, 27, 153, 174, 70, 50, 88, 56, 82, 73, 9, 173, 132, 48, 117, 34, 142, 43, 155, 19, 39, 112, 64, 89, 46, 77, 170, 10, 102, 13, 28, 94, 169, 109, 146, 177, 115, 66, 135, 49, 131, 63, 166, 12, 116, 5, 138, 55, 72, 41, 149, 16, 1, 8, 18, and 25.

FIG. 278 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM and the code rate r is 13/15.

According to the original GW pattern (B) of FIG. 278, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 59, 85, 108, 128, 49, 91, 163, 3, 58, 16, 106, 126, 74, 141, 167, 35, 57, 82, 30, 123, 68, 95, 160, 42, 62, 21, 102, 131, 52, 142, 157, 10, 55, 79, 24, 130, 73, 92, 179, 2, 61, 11, 104, 122, 45, 140, 159, 43, 148, 19, 23, 111, 76, 135, 169, 39, 63, 77, 25, 117, 75, 94, 155, 5, 145, 14, 26, 127, 46, 138, 158, 38, 64, 86, 105, 118, 50, 137, 175, 7, 144, 84, 22, 113, 54, 98, 172, 9, 146, 17, 27, 114, 51, 139, 156, 37, 147, 78, 103, 115, 66, 97, 168, 34, 60, 83, 107, 121, 48, 93, 174, 33, 65, 87, 99, 124, 71, 136, 154, 0, 150, 20, 101, 112, 70, 96, 170, 1, 149, 80, 28, 125, 53, 90, 173, 6, 153, 13, 29, 116, 72, 88, 165, 8, 143, 12, 31, 119, 47, 89, 164, 40, 151, 81, 109, 110, 44, 134, 162, 36, 152, 15, 100, 129, 67, 133, 166, 41, 56, 18, 32, 120, 69, 132, 161, 4, 177, 176, 178, and 171.

According to the converted GW pattern (A) of FIG. 278, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 59, 58, 57, 62, 55, 61, 148, 63, 145, 64, 144, 146, 147, 60, 65, 150, 149, 153, 143, 151, 152, 56, 85, 16, 82, 21, 79, 11, 19, 77, 14, 86, 84, 17, 78, 83, 87, 20, 80, 13, 12, 81, 15, 18, 108, 106, 30, 102, 24, 104, 23, 25, 26, 105, 22, 27, 103, 107, 99, 101, 28, 29, 31, 109, 100, 32, 128, 126, 123, 131, 130, 122, 111, 117, 127, 118, 113, 114, 115, 121, 124, 112, 125, 116, 119, 110, 129, 120, 49, 74, 68, 52, 73, 45, 76, 75, 46, 50, 54, 51, 66, 48, 71, 70, 53, 72, 47, 44, 67, 69, 91, 141, 95, 142, 92, 140, 135, 94, 138, 137, 98, 139, 97, 93, 136, 96, 90, 88, 89, 134, 133, 132, 163, 167, 160, 157, 179, 159, 169, 155, 158, 175, 172, 156, 168, 174, 154, 170, 173, 165, 164, 162, 166, 161, 3, 35, 42, 10, 2, 43, 39, 5, 38, 7, 9, 37, 34, 33, 0, 1, 6, 8, 40, 36, 41, 4, 177, 176, 178, and 171.

FIG. 279 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 279, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 157, 25, 107, 160, 37, 138, 111, 35, 29, 44, 15, 162, 66, 20, 49, 126, 89, 147, 159, 174, 142, 26, 146, 10, 164, 152, 57, 110, 83, 167, 169, 16, 6, 172, 62, 173, 7, 145, 4, 67, 115, 50, 39, 72, 79, 74, 40, 132, 42, 30, 163, 161, 55, 143, 63, 117, 86, 121, 2, 28, 69, 150, 24, 177, 43, 158, 27, 21, 128, 46, 118, 114, 127, 135, 92, 76, 19, 94, 179, 3, 52, 101, 137, 84, 73, 108, 91, 120, 47, 1, 102, 58, 68, 82, 59, 119, 64, 31, 61, 105, 103, 151, 124, 70, 8, 155, 90, 166, 41, 45, 178, 113, 140, 75, 148, 109, 100, 125, 11, 116, 34, 36, 176, 170, 156, 136, 171, 122, 78, 87, 106, 123, 149, 17, 99, 175, 18, 9, 165, 153, 12, 81, 77, 60, 93, 104, 13, 5, 88, 96, 141, 133, 154, 144, 48, 97, 23, 14, 98, 53, 134, 112, 65, 0, 130, 32, 168, 33, 131, 22, 38, 56, 80, 95, 71, 85, 139, 129, 51, and 54.

According to the converted GW pattern (B) of FIG. 279, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 157, 159, 7, 63, 127, 102, 41, 171, 93, 65, 25, 174, 145, 117, 135, 58, 45, 122, 104, 0, 107, 142, 4, 86, 92, 68, 178, 78, 13, 130, 160, 26, 67, 121, 76, 82, 113, 87, 5, 32, 37, 146, 115, 2, 19, 59, 140, 106, 88, 168, 138, 10, 50, 28, 94, 119, 75, 123, 96, 33, 111, 164, 39, 69, 179, 64, 148, 149, 141, 131, 35, 152, 72, 150, 3, 31, 109, 17, 133, 22, 29, 57, 79, 24, 52, 61, 100, 99, 154, 38, 44, 110, 74, 177, 101, 105, 125, 175, 144, 56, 15, 83, 40, 43, 137, 103, 11, 18, 48, 80, 162, 167, 132, 158, 84, 151, 116, 9, 97, 95, 66, 169, 42, 27, 73, 124, 34, 165, 23, 71, 20, 16, 30, 21, 108, 70, 36, 153, 14, 85, 49, 6, 163, 128, 91, 8, 176, 12, 98, 139, 126, 172, 161, 46, 120, 155, 170, 81, 53, 129, 89, 62, 55, 118, 47, 90, 156, 77, 134, 51, 147, 173, 143, 114, 1, 166, 136, 60, 112, and 54.

FIG. 280 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 280, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 113, 153, 13, 8, 103, 115, 137, 69, 151, 111, 18, 38, 42, 150, 179, 130, 148, 6, 4, 31, 44, 68, 145, 126, 106, 24, 100, 93, 21, 35, 143, 57, 166, 65, 53, 41, 122, 7, 29, 25, 136, 162, 158, 26, 124, 32, 17, 168, 56, 12, 39, 176, 131, 132, 51, 89, 101, 160, 49, 87, 14, 55, 127, 37, 169, 110, 83, 134, 107, 46, 33, 114, 108, 82, 125, 109, 95, 174, 62, 164, 144, 16, 121, 58, 80, 2, 163, 159, 157, 90, 104, 23, 172, 112, 19, 133, 102, 75, 45, 86, 63, 22, 54, 105, 155, 77, 178, 70, 98, 40, 118, 84, 78, 0, 99, 123, 5, 34, 71, 96, 175, 10, 30, 72, 28, 74, 154, 61, 91, 85, 135, 152, 15, 88, 165, 60, 52, 149, 147, 59, 116, 120, 3, 64, 140, 67, 94, 27, 9, 81, 43, 11, 167, 139, 92, 129, 20, 117, 128, 50, 119, 47, 1, 156, 142, 170, 171, 48, 177, 66, 161, 79, 73, 76, 173, 97, 36, 141, 146, and 138.

According to the converted GW pattern (B) of FIG. 280, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 113, 4, 122, 51, 108, 104, 98, 154, 140, 1, 153, 31, 7, 89, 82, 23, 40, 61, 67, 156, 13, 44, 29, 101, 125, 172, 118, 91, 94, 142, 8, 68, 25, 160, 109, 112, 84, 85, 27, 170, 103, 145, 136, 49, 95, 19, 78, 135, 9, 171, 115, 126, 162, 87, 174, 133, 0, 152, 81, 48, 137, 106, 158, 14, 62, 102, 99, 15, 43, 177, 69, 24, 26, 55, 164, 75, 123, 88, 11, 66, 151, 100, 124, 127, 144, 45, 5, 165, 167, 161, 111, 93, 32, 37, 16, 86, 34, 60, 139, 79, 18, 21, 17, 169, 121, 63, 71, 52, 92, 73, 38, 35, 168, 110, 58, 22, 96, 149, 129, 76, 42, 143, 56, 83, 80, 54, 175, 147, 20, 173, 150, 57, 12, 134, 2, 105, 10, 59, 117, 97, 179, 166, 39, 107, 163, 155, 30, 116, 128, 36, 130, 65, 176, 46, 159, 77, 72, 120, 50, 141, 148, 53, 131, 33, 157, 178, 28, 3, 119, 146, 6, 41, 132, 114, 90, 70, 74, 64, 47, and 138.

FIG. 281 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 281, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 114, 133, 4, 73, 8, 139, 7, 5, 177, 88, 66, 11, 24, 74, 49, 45, 167, 81, 117, 137, 46, 22, 165, 51, 68, 110, 6, 1, 16, 132, 130, 143, 169, 2, 20, 140, 94, 21, 91, 126, 172, 27, 162, 34, 113, 142, 166, 115, 106, 160, 84, 136, 175, 0, 26, 151, 69, 174, 59, 159, 161, 170, 52, 164, 80, 108, 3, 23, 101, 33, 125, 111, 63, 124, 98, 40, 145, 9, 39, 155, 149, 147, 67, 76, 48, 120, 119, 53, 54, 138, 179, 156, 127, 13, 152, 129, 123, 141, 109, 89, 121, 50, 10, 37, 104, 144, 86, 178, 96, 148, 128, 56, 64, 153, 95, 12, 105, 41, 154, 99, 25, 171, 92, 17, 134, 19, 61, 32, 85, 102, 14, 71, 146, 163, 173, 118, 57, 18, 36, 42, 78, 31, 97, 55, 58, 116, 90, 168, 43, 72, 15, 112, 93, 60, 38, 103, 87, 158, 35, 29, 176, 150, 77, 79, 122, 47, 28, 135, 100, 83, 65, 131, 75, 157, 62, 70, 44, 30, 107, and 82.

According to the converted GW pattern (B) of FIG. 281, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 114, 117, 94, 26, 63, 179, 96, 61, 58, 77, 133, 137, 21, 151, 124, 156, 148, 32, 116, 79, 4, 46, 91, 69, 98, 127, 128, 85, 90, 122, 73, 22, 126, 174, 40, 13, 56, 102, 168, 47, 8, 165, 172, 59, 145, 152, 64, 14, 43, 28, 139, 51, 27, 159, 9, 129, 153, 71, 72, 135, 7, 68, 162, 161, 39, 123, 95, 146, 15, 100, 5, 110, 34, 170, 155, 141, 12, 163, 112, 83, 177, 6, 113, 52, 149, 109, 105, 173, 93, 65, 88, 1, 142, 164, 147, 89, 41, 118, 60, 131, 66, 16, 166, 80, 67, 121, 154, 57, 38, 75, 11, 132, 115, 108, 76, 50, 99, 18, 103, 157, 24, 130, 106, 3, 48, 10, 25, 36, 87, 62, 74, 143, 160, 23, 120, 37, 171, 42, 158, 70, 49, 169, 84, 101, 119, 104, 92, 78, 35, 44, 45, 2, 136, 33, 53, 144, 17, 31, 29, 30, 167, 20, 175, 125, 54, 86, 134, 97, 176, 107, 81, 140, 0, 111, 138, 178, 19, 55, 150, and 82.

FIG. 282 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 5/15.

According to the original GW pattern (B) of FIG. 282, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 128, 4, 162, 8, 77, 29, 91, 44, 176, 107, 149, 1, 150, 9, 119, 99, 71, 124, 104, 41, 62, 5, 118, 50, 174, 54, 111, 40, 156, 92, 46, 11, 17, 52, 47, 97, 179, 24, 153, 145, 129, 2, 12, 88, 101, 139, 114, 69, 96, 32, 134, 55, 167, 132, 123, 136, 112, 102, 159, 31, 87, 141, 15, 61, 84, 98, 37, 63, 20, 85, 53, 7, 39, 117, 170, 138, 116, 126, 161, 120, 57, 13, 76, 6, 121, 155, 175, 38, 158, 35, 86, 78, 10, 103, 166, 95, 125, 172, 67, 30, 177, 73, 151, 169, 163, 23, 108, 43, 81, 157, 58, 105, 65, 26, 122, 135, 146, 72, 142, 34, 133, 0, 148, 89, 168, 60, 109, 83, 18, 27, 131, 70, 56, 48, 64, 93, 68, 127, 21, 75, 110, 80, 14, 49, 82, 143, 115, 178, 154, 100, 59, 74, 152, 51, 137, 140, 36, 42, 19, 25, 94, 45, 164, 16, 113, 79, 22, 28, 66, 106, 130, 171, 147, 90, 144, 165, 3, 173, 160, and 33.

According to the converted GW pattern (A) of FIG. 282, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 128, 149, 62, 46, 129, 134, 87, 53, 57, 86, 177, 58, 133, 131, 110, 59, 94, 130, 4, 1, 5, 11, 2, 55, 141, 7, 13, 78, 73, 105, 0, 70, 80, 74, 45, 171, 162, 150, 118, 17, 12, 167, 15, 39, 76, 10, 151, 65, 148, 56, 14, 152, 164, 147, 8, 9, 50, 52, 88, 132, 61, 117, 6, 103, 169, 26, 89, 48, 49, 51, 16, 90, 77, 119, 174, 47, 101, 123, 84, 170, 121, 166, 163, 122, 168, 64, 82, 137, 113, 144, 29, 99, 54, 97, 139, 136, 98, 138, 155, 95, 23, 135, 60, 93, 143, 140, 79, 165, 91, 71, 111, 179, 114, 112, 37, 116, 175, 125, 108, 146, 109, 68, 115, 36, 22, 3, 44, 124, 40, 24, 69, 102, 63, 126, 38, 172, 43, 72, 83, 127, 178, 42, 28, 173, 176, 104, 156, 153, 96, 159, 20, 161, 158, 67, 81, 142, 18, 21, 154, 19, 66, 160, 107, 41, 92, 145, 32, 31, 85, 120, 35, 30, 157, 34, 27, 75, 100, 25, 106, and 33.

FIG. 283 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 6/15.

According to the original GW pattern (A) of FIG. 283, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 66, 21, 51, 55, 54, 24, 33, 12, 70, 63, 47, 65, 145, 8, 0, 57, 23, 71, 59, 14, 40, 42, 62, 56, 2, 43, 64, 58, 67, 53, 68, 61, 39, 52, 69, 1, 22, 31, 161, 38, 30, 19, 17, 18, 4, 41, 25, 44, 136, 29, 36, 26, 126, 177, 15, 37, 148, 9, 13, 45, 46, 152, 50, 49, 27, 77, 60, 35, 48, 178, 28, 34, 106, 127, 76, 131, 105, 138, 75, 130, 101, 167, 117, 173, 113, 108, 92, 135, 124, 121, 97, 149, 143, 81, 32, 96, 3, 78, 107, 86, 98, 16, 162, 150, 111, 158, 172, 139, 74, 142, 166, 7, 5, 119, 20, 144, 151, 90, 11, 156, 100, 175, 83, 155, 159, 128, 88, 87, 93, 103, 94, 140, 165, 6, 137, 157, 10, 85, 141, 129, 146, 122, 73, 112, 132, 125, 174, 169, 168, 79, 84, 118, 179, 147, 91, 160, 163, 115, 89, 80, 102, 104, 134, 82, 95, 133, 164, 154, 120, 110, 170, 114, 153, 72, 109, 171, 176, 99, 116, and 123.

According to the converted GW pattern (B) of FIG. 283, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 66, 59, 22, 15, 106, 97, 74, 88, 132, 134, 21, 14, 31, 37, 127, 149, 142, 87, 125, 82, 51, 40, 161, 148, 76, 143, 166, 93, 174, 95, 55, 42, 38, 9, 131, 81, 7, 103, 169, 133, 54, 62, 30, 13, 105, 32, 5, 94, 168, 164, 24, 56, 19, 45, 138, 96, 119, 140, 79, 154, 33, 2, 17, 46, 75, 3, 20, 165, 84, 120, 12, 43, 18, 152, 130, 78, 144, 6, 118, 110, 70, 64, 4, 50, 101, 107, 151, 137, 179, 170, 63, 58, 41, 49, 167, 86, 90, 157, 147, 114, 47, 67, 25, 27, 117, 98, 11, 10, 91, 153, 65, 53, 44, 77, 173, 16, 156, 85, 160, 72, 145, 68, 136, 60, 113, 162, 100, 141, 163, 109, 8, 61, 29, 35, 108, 150, 175, 129, 115, 171, 0, 39, 36, 48, 92, 111, 83, 146, 89, 176, 57, 52, 26, 178, 135, 158, 155, 122, 80, 99, 23, 69, 126, 28, 124, 172, 159, 73, 102, 116, 71, 1, 177, 34, 121, 139, 128, 112, 104, and 123.

FIG. 284 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 284, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 117, 61, 46, 179, 24, 161, 142, 133, 11, 6, 121, 44, 103, 76, 22, 63, 136, 151, 33, 8, 123, 60, 105, 175, 18, 160, 138, 147, 10, 0, 125, 57, 49, 75, 21, 154, 140, 150, 9, 169, 124, 55, 48, 173, 23, 157, 97, 129, 30, 7, 122, 54, 99, 74, 19, 153, 94, 128, 15, 170, 87, 59, 51, 80, 111, 64, 137, 146, 13, 2, 83, 62, 45, 176, 108, 71, 91, 131, 34, 168, 82, 56, 102, 72, 26, 155, 92, 132, 31, 166, 119, 36, 101, 178, 113, 67, 98, 152, 14, 5, 118, 41, 104, 177, 114, 70, 96, 134, 32, 162, 84, 40, 100, 174, 110, 158, 93, 149, 27, 4, 86, 38, 53, 77, 115, 159, 143, 130, 35, 163, 89, 58, 106, 73, 20, 66, 90, 127, 16, 3, 85, 37, 107, 172, 116, 156, 95, 144, 17, 165, 81, 43, 50, 78, 109, 68, 135, 126, 29, 167, 120, 39, 47, 171, 112, 69, 141, 145, 28, 1, 88, 42, 52, 79, 25, 65, 139, 148, 12, and 164.

According to the converted GW pattern (A) of FIG. 284, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 117, 121, 123, 125, 124, 122, 87, 83, 82, 119, 118, 84, 86, 89, 85, 81, 120, 88, 61, 44, 60, 57, 55, 54, 59, 62, 56, 36, 41, 40, 38, 58, 37, 43, 39, 42, 46, 103, 105, 49, 48, 99, 51, 45, 102, 101, 104, 100, 53, 106, 107, 50, 47, 52, 179, 76, 175, 75, 173, 74, 80, 176, 72, 178, 177, 174, 77, 73, 172, 78, 171, 79, 24, 22, 18, 21, 23, 19, 111, 108, 26, 113, 114, 110, 115, 20, 116, 109, 112, 25, 161, 63, 160, 154, 157, 153, 64, 71, 155, 67, 70, 158, 159, 66, 156, 68, 69, 65, 142, 136, 138, 140, 97, 94, 137, 91, 92, 98, 96, 93, 143, 90, 95, 135, 141, 139, 133, 151, 147, 150, 129, 128, 146, 131, 132, 152, 134, 149, 130, 127, 144, 126, 145, 148, 11, 33, 10, 9, 30, 15, 13, 34, 31, 14, 32, 27, 35, 16, 17, 29, 28, 12, 6, 8, 0, 169, 7, 170, 2, 168, 166, 5, 162, 4, 163, 3, 165, 167, 1, and 164.

FIG. 285 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 285, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 48, 82, 51, 57, 69, 65, 6, 71, 90, 84, 81, 50, 88, 61, 55, 53, 73, 39, 13, 79, 75, 41, 18, 38, 89, 49, 93, 36, 64, 47, 40, 42, 76, 70, 56, 3, 72, 2, 54, 52, 145, 19, 78, 80, 63, 87, 67, 86, 10, 1, 58, 17, 14, 175, 91, 68, 85, 94, 15, 43, 74, 60, 66, 37, 92, 4, 9, 16, 83, 46, 44, 102, 30, 112, 122, 110, 29, 20, 105, 138, 101, 174, 33, 137, 136, 131, 166, 59, 34, 62, 125, 28, 26, 45, 24, 23, 21, 157, 98, 35, 95, 22, 32, 103, 27, 113, 31, 119, 173, 168, 118, 120, 114, 149, 159, 155, 179, 160, 161, 130, 123, 172, 139, 124, 153, 0, 109, 167, 128, 107, 117, 147, 177, 96, 164, 152, 11, 148, 158, 129, 163, 176, 151, 171, 8, 106, 144, 150, 169, 108, 162, 143, 111, 141, 133, 178, 134, 146, 99, 132, 142, 104, 115, 135, 121, 100, 12, 170, 156, 126, 5, 127, 154, 97, 140, 116, 165, 7, and 25.

According to the converted GW pattern (B) of FIG. 285, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 39, 3, 175, 102, 62, 119, 0, 171, 104, 48, 13, 72, 91, 30, 125, 173, 109, 8, 115, 82, 79, 2, 68, 112, 28, 168, 167, 106, 135, 51, 75, 54, 85, 122, 26, 118, 128, 144, 121, 57, 41, 52, 94, 110, 45, 120, 107, 150, 100, 69, 18, 145, 15, 29, 24, 114, 117, 169, 12, 65, 38, 19, 43, 20, 23, 149, 147, 108, 170, 6, 89, 78, 74, 105, 21, 159, 177, 162, 156, 71, 49, 80, 60, 138, 157, 155, 96, 143, 126, 90, 93, 63, 66, 101, 98, 179, 164, 111, 5, 84, 36, 87, 37, 174, 35, 160, 152, 141, 127, 81, 64, 67, 92, 33, 95, 161, 11, 133, 154, 50, 47, 86, 4, 137, 22, 130, 148, 178, 97, 88, 40, 10, 9, 136, 32, 123, 158, 134, 140, 61, 42, 1, 16, 131, 103, 172, 129, 146, 116, 55, 76, 58, 83, 166, 27, 139, 163, 99, 165, 53, 70, 17, 46, 59, 113, 124, 176, 132, 7, 73, 56, 14, 44, 34, 31, 153, 151, 142, and 25.

FIG. 286 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 286, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 42, 36, 135, 126, 3, 17, 82, 87, 172, 32, 65, 70, 143, 131, 10, 1, 85, 147, 31, 176, 66, 47, 97, 128, 8, 9, 146, 73, 162, 164, 57, 64, 139, 91, 5, 110, 150, 83, 18, 27, 48, 45, 133, 132, 111, 124, 89, 78, 177, 19, 46, 50, 102, 103, 122, 4, 74, 161, 175, 34, 60, 58, 136, 100, 115, 118, 81, 75, 28, 21, 40, 61, 140, 138, 113, 112, 157, 151, 23, 30, 69, 41, 94, 96, 7, 109, 152, 149, 33, 179, 71, 43, 92, 105, 12, 13, 154, 159, 178, 24, 44, 49, 107, 98, 16, 2, 76, 155, 35, 168, 62, 56, 129, 141, 116, 123, 160, 77, 25, 170, 54, 39, 90, 95, 121, 11, 72, 153, 169, 167, 51, 67, 104, 134, 0, 117, 79, 80, 26, 29, 37, 55, 99, 142, 108, 114, 86, 88, 166, 163, 59, 63, 101, 93, 119, 15, 144, 145, 165, 22, 52, 53, 130, 137, 125, 6, 158, 84, 20, 174, 38, 68, 127, 106, 14, 120, 148, 156, 171, and 173.

According to the converted GW pattern (A) of FIG. 286, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 42, 65, 66, 57, 48, 46, 60, 40, 69, 71, 44, 62, 54, 51, 37, 59, 52, 38, 36, 70, 47, 64, 45, 50, 58, 61, 41, 43, 49, 56, 39, 67, 55, 63, 53, 68, 135, 143, 97, 139, 133, 102, 136, 140, 94, 92, 107, 129, 90, 104, 99, 101, 130, 127, 126, 131, 128, 91, 132, 103, 100, 138, 96, 105, 98, 141, 95, 134, 142, 93, 137, 106, 3, 10, 8, 5, 111, 122, 115, 113, 7, 12, 16, 116, 121, 0, 108, 119, 125, 14, 17, 1, 9, 110, 124, 4, 118, 112, 109, 13, 2, 123, 11, 117, 114, 15, 6, 120, 82, 85, 146, 150, 89, 74, 81, 157, 152, 154, 76, 160, 72, 79, 86, 144, 158, 148, 87, 147, 73, 83, 78, 161, 75, 151, 149, 159, 155, 77, 153, 80, 88, 145, 84, 156, 172, 31, 162, 18, 177, 175, 28, 23, 33, 178, 35, 25, 169, 26, 166, 165, 20, 171, 32, 176, 164, 27, 19, 34, 21, 30, 179, 24, 168, 170, 167, 29, 163, 22, 174, and 173.

FIG. 287 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 10/15.

According to the original GW pattern (B) of FIG. 287, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 100, 22, 60, 121, 40, 44, 164, 170, 176, 101, 88, 26, 35, 4, 21, 173, 140, 145, 175, 174, 81, 28, 72, 112, 132, 106, 42, 56, 151, 147, 82, 49, 91, 64, 179, 89, 160, 52, 139, 17, 97, 63, 116, 131, 154, 71, 109, 96, 135, 146, 55, 38, 166, 117, 65, 127, 120, 129, 15, 136, 74, 23, 98, 43, 123, 130, 69, 99, 143, 161, 46, 51, 94, 61, 83, 67, 156, 33, 144, 148, 163, 47, 92, 2, 122, 24, 86, 75, 108, 152, 14, 77, 7, 10, 29, 19, 104, 128, 142, 1, 79, 107, 162, 0, 118, 66, 54, 153, 141, 9, 85, 37, 32, 114, 53, 134, 41, 158, 178, 138, 76, 50, 78, 84, 172, 48, 133, 168, 125, 13, 169, 25, 16, 8, 124, 159, 167, 58, 5, 11, 68, 95, 27, 110, 93, 62, 102, 137, 126, 150, 87, 105, 113, 30, 119, 6, 103, 57, 31, 149, 80, 70, 45, 165, 111, 73, 36, 157, 171, 3, 20, 18, 90, 12, 59, 39, 115, 34, 177, and 155.

According to the converted GW pattern (A) of FIG. 287, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 100, 88, 81, 82, 97, 55, 74, 46, 163, 14, 79, 85, 76, 169, 68, 87, 80, 20, 22, 26, 28, 49, 63, 38, 23, 51, 47, 77, 107, 37, 50, 25, 95, 105, 70, 18, 60, 35, 72, 91, 116, 166, 98, 94, 92, 7, 162, 32, 78, 16, 27, 113, 45, 90, 121, 4, 112, 64, 131, 117, 43, 61, 2, 10, 0, 114, 84, 8, 110, 30, 165, 12, 40, 21, 132, 179, 154, 65, 123, 83, 122, 29, 118, 53, 172, 124, 93, 119, 111, 59, 44, 173, 106, 89, 71, 127, 130, 67, 24, 19, 66, 134, 48, 159, 62, 6, 73, 39, 164, 140, 42, 160, 109, 120, 69, 156, 86, 104, 54, 41, 133, 167, 102, 103, 36, 115, 170, 145, 56, 52, 96, 129, 99, 33, 75, 128, 153, 158, 168, 58, 137, 57, 157, 34, 176, 175, 151, 139, 135, 15, 143, 144, 108, 142, 141, 178, 125, 5, 126, 31, 171, 177, 101, 174, 147, 17, 146, 136, 161, 148, 152, 1, 9, 138, 13, 11, 150, 149, 3, and 155.

FIG. 288 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 11/15.

According to the original GW pattern (B) of FIG. 288, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 33, 73, 90, 107, 99, 94, 53, 151, 124, 8, 12, 117, 21, 58, 158, 77, 72, 59, 123, 2, 125, 157, 50, 62, 109, 75, 42, 146, 118, 153, 85, 10, 131, 70, 32, 41, 24, 143, 113, 1, 93, 162, 20, 35, 74, 45, 149, 161, 173, 4, 28, 23, 127, 148, 34, 61, 96, 144, 171, 140, 119, 16, 126, 39, 40, 57, 165, 106, 172, 139, 81, 47, 164, 92, 63, 105, 108, 170, 3, 135, 101, 121, 68, 6, 111, 65, 147, 150, 122, 7, 84, 46, 22, 103, 86, 169, 134, 44, 175, 167, 89, 128, 27, 31, 56, 43, 102, 156, 160, 141, 67, 9, 110, 159, 133, 78, 154, 176, 174, 5, 82, 11, 25, 80, 130, 163, 88, 36, 166, 137, 104, 48, 129, 87, 95, 55, 49, 145, 178, 0, 98, 64, 54, 100, 37, 79, 69, 38, 177, 136, 114, 17, 52, 19, 30, 97, 51, 168, 132, 138, 83, 76, 13, 18, 115, 71, 91, 179, 112, 155, 15, 14, 26, 60, 29, 116, 66, 120, 142, and 152.

According to the converted GW pattern (A) of FIG. 288, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 33, 12, 125, 85, 93, 28, 119, 81, 101, 84, 89, 67, 82, 104, 98, 114, 83, 15, 73, 117, 157, 10, 162, 23, 16, 47, 121, 46, 128, 9, 11, 48, 64, 17, 76, 14, 90, 21, 50, 131, 20, 127, 126, 164, 68, 22, 27, 110, 25, 129, 54, 52, 13, 26, 107, 58, 62, 70, 35, 148, 39, 92, 6, 103, 31, 159, 80, 87, 100, 19, 18, 60, 99, 158, 109, 32, 74, 34, 40, 63, 111, 86, 56, 133, 130, 95, 37, 30, 115, 29, 94, 77, 75, 41, 45, 61, 57, 105, 65, 169, 43, 78, 163, 55, 79, 97, 71, 116, 53, 72, 42, 24, 149, 96, 165, 108, 147, 134, 102, 154, 88, 49, 69, 51, 91, 66, 151, 59, 146, 143, 161, 144, 106, 170, 150, 44, 156, 176, 36, 145, 38, 168, 179, 120, 124, 123, 118, 113, 173, 171, 172, 3, 122, 175, 160, 174, 166, 178, 177, 132, 112, 142, 8, 2, 153, 1, 4, 140, 139, 135, 7, 167, 141, 5, 137, 0, 136, 138, 155, and 152.

FIG. 289 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 289, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 91, 19, 11, 106, 14, 40, 20, 67, 32, 22, 31, 23, 78, 68, 79, 141, 117, 95, 88, 136, 52, 121, 1, 133, 4, 2, 21, 122, 38, 12, 69, 111, 81, 82, 58, 46, 112, 60, 33, 73, 53, 92, 75, 48, 47, 110, 80, 76, 138, 87, 85, 65, 130, 57, 102, 83, 64, 86, 100, 39, 49, 125, 108, 119, 6, 118, 35, 61, 71, 30, 45, 94, 26, 116, 98, 37, 55, 44, 70, 25, 7, 34, 114, 135, 128, 137, 84, 51, 28, 97, 27, 89, 29, 62, 50, 139, 56, 109, 77, 59, 127, 142, 96, 105, 99, 90, 13, 124, 120, 115, 126, 143, 149, 74, 41, 178, 129, 18, 131, 42, 165, 101, 134, 36, 140, 132, 103, 72, 164, 93, 54, 166, 43, 123, 113, 0, 154, 10, 63, 107, 162, 157, 66, 104, 17, 147, 167, 174, 179, 3, 173, 160, 155, 161, 152, 156, 177, 24, 170, 9, 159, 16, 15, 148, 5, 146, 163, 172, 175, 151, 169, 176, 150, 153, 171, 158, 168, 144, 8, and 145.

According to the converted GW pattern (B) of FIG. 289, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 91, 88, 112, 102, 26, 27, 120, 103, 17, 15, 19, 136, 60, 83, 116, 89, 115, 72, 147, 148, 11, 52, 33, 64, 98, 29, 126, 164, 167, 5, 106, 121, 73, 86, 37, 62, 143, 93, 174, 146, 14, 1, 53, 100, 55, 50, 149, 54, 179, 163, 40, 133, 92, 39, 44, 139, 74, 166, 3, 172, 20, 4, 75, 49, 70, 56, 41, 43, 173, 175, 67, 2, 48, 125, 25, 109, 178, 123, 160, 151, 32, 21, 47, 108, 7, 77, 129, 113, 155, 169, 22, 122, 110, 119, 34, 59, 18, 0, 161, 176, 31, 38, 80, 6, 114, 127, 131, 154, 152, 150, 23, 12, 76, 118, 135, 142, 42, 10, 156, 153, 78, 69, 138, 35, 128, 96, 165, 63, 177, 171, 68, 111, 87, 61, 137, 105, 101, 107, 24, 158, 79, 81, 85, 71, 84, 99, 134, 162, 170, 168, 141, 82, 65, 30, 51, 90, 36, 157, 9, 144, 117, 58, 130, 45, 28, 13, 140, 66, 159, 8, 95, 46, 57, 94, 97, 124, 132, 104, 16, and 145.

FIG. 290 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 290, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175.

According to the converted GW pattern (B) of FIG. 290, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 49, 56, 3, 62, 103, 136, 150, 148, 18, 159, 2, 38, 75, 64, 95, 90, 106, 151, 170, 171, 57, 48, 73, 74, 101, 88, 146, 113, 164, 161, 47, 32, 65, 70, 143, 94, 130, 126, 20, 118, 31, 50, 145, 82, 9, 10, 27, 124, 140, 17, 35, 23, 71, 149, 89, 8, 108, 135, 160, 163, 24, 34, 79, 76, 141, 14, 153, 129, 166, 21, 39, 54, 67, 4, 128, 96, 112, 109, 162, 165, 59, 1, 69, 78, 97, 104, 114, 25, 119, 19, 0, 36, 83, 84, 137, 92, 29, 28, 155, 179, 45, 44, 85, 80, 133, 132, 110, 158, 168, 177, 41, 52, 147, 86, 7, 142, 134, 117, 178, 167, 55, 40, 63, 66, 13, 100, 116, 105, 22, 138, 53, 58, 81, 68, 99, 98, 15, 115, 174, 173, 51, 122, 77, 72, 91, 12, 127, 111, 172, 156, 37, 46, 61, 6, 93, 102, 125, 131, 176, 144, 33, 42, 5, 60, 87, 152, 123, 107, 16, 169, 43, 30, 26, 154, 11, 139, 120, 121, 157, and 175.

FIG. 291 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 291, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 14, 129, 71, 96, 171, 36, 144, 64, 162, 4, 86, 128, 113, 7, 105, 131, 2, 133, 106, 79, 11, 152, 26, 118, 158, 126, 17, 55, 45, 111, 138, 84, 6, 52, 167, 38, 20, 101, 31, 120, 5, 112, 74, 69, 121, 9, 154, 15, 146, 116, 63, 1, 114, 83, 124, 109, 39, 75, 123, 57, 49, 30, 21, 40, 43, 77, 157, 44, 13, 99, 34, 147, 166, 56, 155, 176, 95, 102, 119, 161, 37, 159, 97, 68, 122, 163, 89, 61, 107, 22, 10, 127, 87, 103, 179, 172, 66, 59, 8, 145, 88, 132, 110, 54, 47, 153, 25, 32, 73, 42, 148, 150, 28, 91, 18, 24, 19, 53, 136, 48, 76, 35, 151, 173, 149, 142, 160, 94, 117, 169, 165, 141, 80, 67, 170, 164, 82, 65, 60, 135, 168, 23, 100, 134, 90, 98, 125, 85, 137, 81, 41, 156, 50, 3, 29, 16, 72, 177, 0, 78, 62, 139, 93, 46, 12, 175, 130, 51, 178, 92, 115, 174, 27, 70, 58, 33, 104, 140, 108, and 143.

According to the converted GW pattern (B) of FIG. 291, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 14, 131, 138, 9, 49, 176, 10, 153, 76, 164, 41, 175, 129, 2, 84, 154, 30, 95, 127, 25, 35, 82, 156, 130, 71, 133, 6, 15, 21, 102, 87, 32, 151, 65, 50, 51, 96, 106, 52, 146, 40, 119, 103, 73, 173, 60, 3, 178, 171, 79, 167, 116, 43, 161, 179, 42, 149, 135, 29, 92, 36, 11, 38, 63, 77, 37, 172, 148, 142, 168, 16, 115, 144, 152, 20, 1, 157, 159, 66, 150, 160, 23, 72, 174, 64, 26, 101, 114, 44, 97, 59, 28, 94, 100, 177, 27, 162, 118, 31, 83, 13, 68, 8, 91, 117, 134, 0, 70, 4, 158, 120, 124, 99, 122, 145, 18, 169, 90, 78, 58, 86, 126, 5, 109, 34, 163, 88, 24, 165, 98, 62, 33, 128, 17, 112, 39, 147, 89, 132, 19, 141, 125, 139, 104, 113, 55, 74, 75, 166, 61, 110, 53, 80, 85, 93, 140, 7, 45, 69, 123, 56, 107, 54, 136, 67, 137, 46, 108, 105, 111, 121, 57, 155, 22, 47, 48, 170, 81, 12, and 143.

FIG. 292 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 292, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 136, 20, 44, 36, 17, 120, 89, 142, 66, 35, 42, 116, 14, 119, 117, 29, 47, 125, 11, 158, 74, 25, 37, 175, 41, 145, 100, 131, 173, 179, 16, 77, 112, 40, 58, 23, 82, 168, 106, 83, 34, 49, 122, 2, 157, 107, 79, 137, 53, 96, 33, 70, 19, 38, 121, 90, 118, 126, 165, 109, 154, 140, 10, 178, 143, 92, 63, 176, 146, 134, 177, 139, 3, 113, 172, 9, 50, 138, 61, 93, 94, 88, 132, 105, 151, 170, 86, 12, 1, 7, 56, 59, 101, 155, 95, 54, 85, 13, 39, 15, 76, 130, 97, 110, 174, 72, 150, 55, 73, 99, 111, 162, 26, 21, 156, 28, 160, 149, 133, 104, 81, 69, 84, 4, 6, 147, 48, 115, 169, 127, 161, 71, 68, 80, 91, 98, 8, 57, 171, 135, 52, 5, 141, 65, 75, 163, 43, 144, 167, 159, 129, 46, 31, 30, 166, 0, 148, 128, 102, 103, 60, 32, 18, 51, 87, 114, 64, 22, 164, 24, 123, 27, 62, 124, 152, 78, 108, 67, 153, and 45.

According to the converted GW pattern (B) of FIG. 292, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 136, 29, 16, 107, 154, 9, 56, 72, 81, 98, 129, 114, 20, 47, 77, 79, 140, 50, 59, 150, 69, 8, 46, 64, 44, 125, 112, 137, 10, 138, 101, 55, 84, 57, 31, 22, 36, 11, 40, 53, 178, 61, 155, 73, 4, 171, 30, 164, 17, 158, 58, 96, 143, 93, 95, 99, 6, 135, 166, 24, 120, 74, 23, 33, 92, 94, 54, 111, 147, 52, 0, 123, 89, 25, 82, 70, 63, 88, 85, 162, 48, 5, 148, 27, 142, 37, 168, 19, 176, 132, 13, 26, 115, 141, 128, 62, 66, 175, 106, 38, 146, 105, 39, 21, 169, 65, 102, 124, 35, 41, 83, 121, 134, 151, 15, 156, 127, 75, 103, 152, 42, 145, 34, 90, 177, 170, 76, 28, 161, 163, 60, 78, 116, 100, 49, 118, 139, 86, 130, 160, 71, 43, 32, 108, 14, 131, 122, 126, 3, 12, 97, 149, 68, 144, 18, 67, 119, 173, 2, 165, 113, 1, 110, 133, 80, 167, 51, 153, 117, 179, 157, 109, 172, 7, 174, 104, 91, 159, 87, and 45.

FIG. 293 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 293, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 91, 52, 36, 30, 35, 6, 121, 29, 150, 47, 163, 2, 89, 39, 65, 157, 64, 122, 101, 40, 84, 69, 90, 129, 10, 9, 15, 162, 21, 171, 43, 44, 132, 158, 104, 4, 72, 169, 177, 103, 76, 28, 78, 53, 1, 151, 161, 88, 148, 42, 160, 109, 100, 126, 138, 108, 38, 25, 3, 112, 17, 124, 155, 172, 134, 86, 119, 94, 145, 178, 68, 26, 130, 140, 115, 152, 139, 37, 22, 102, 14, 118, 11, 98, 154, 61, 146, 164, 107, 131, 159, 63, 93, 7, 79, 5, 137, 165, 59, 77, 55, 80, 117, 13, 173, 144, 85, 153, 66, 106, 49, 34, 48, 41, 143, 142, 27, 136, 18, 111, 175, 123, 147, 114, 19, 125, 166, 149, 113, 46, 31, 141, 120, 57, 74, 8, 20, 96, 170, 128, 97, 16, 60, 110, 156, 45, 82, 105, 62, 99, 23, 92, 32, 50, 73, 56, 167, 95, 24, 168, 33, 116, 75, 127, 81, 67, 179, 174, 70, 12, 58, 87, 176, 0, 51, 135, 83, 133, 54, and 71.

According to the converted GW pattern (B) of FIG. 293, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 91, 157, 43, 151, 17, 152, 159, 144, 175, 8, 23, 67, 52, 64, 44, 161, 124, 139, 63, 85, 123, 20, 92, 179, 36, 122, 132, 88, 155, 37, 93, 153, 147, 96, 32, 174, 30, 101, 158, 148, 172, 22, 7, 66, 114, 170, 50, 70, 35, 40, 104, 42, 134, 102, 79, 106, 19, 128, 73, 12, 6, 84, 4, 160, 86, 14, 5, 49, 125, 97, 56, 58, 121, 69, 72, 109, 119, 118, 137, 34, 166, 16, 167, 87, 29, 90, 169, 100, 94, 11, 165, 48, 149, 60, 95, 176, 150, 129, 177, 126, 145, 98, 59, 41, 113, 110, 24, 0, 47, 10, 103, 138, 178, 154, 77, 143, 46, 156, 168, 51, 163, 9, 76, 108, 68, 61, 55, 142, 31, 45, 33, 135, 2, 15, 28, 38, 26, 146, 80, 27, 141, 82, 116, 83, 89, 162, 78, 25, 130, 164, 117, 136, 120, 105, 75, 133, 39, 21, 53, 3, 140, 107, 13, 18, 57, 62, 127, 54, 65, 171, 1, 112, 115, 131, 173, 111, 74, 99, 81, and 71.

FIG. 294 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 294, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 146, 89, 57, 16, 164, 138, 91, 78, 90, 66, 122, 12, 9, 157, 14, 68, 112, 128, 74, 45, 28, 87, 158, 56, 61, 168, 18, 161, 95, 99, 139, 22, 65, 130, 166, 118, 150, 49, 142, 44, 36, 1, 121, 6, 46, 29, 88, 47, 0, 58, 105, 43, 80, 64, 107, 21, 55, 151, 8, 145, 163, 7, 98, 123, 17, 11, 153, 136, 52, 3, 13, 34, 160, 102, 125, 114, 152, 84, 32, 97, 33, 60, 62, 79, 37, 129, 38, 165, 71, 75, 59, 144, 127, 132, 104, 53, 162, 103, 120, 54, 155, 116, 48, 77, 76, 73, 113, 119, 179, 177, 41, 19, 92, 109, 31, 143, 178, 108, 39, 140, 106, 40, 5, 25, 81, 176, 101, 124, 126, 72, 111, 4, 173, 156, 134, 86, 174, 2, 170, 35, 175, 137, 15, 24, 69, 96, 30, 117, 67, 171, 149, 169, 63, 23, 20, 167, 27, 147, 51, 10, 82, 131, 85, 110, 94, 135, 172, 148, 50, 154, 42, 70, 115, 26, 83, 141, 100, 133, 93, and 159.

According to the converted GW pattern (B) of FIG. 294, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 146, 68, 139, 29, 163, 114, 59, 73, 106, 86, 149, 135, 89, 112, 22, 88, 7, 152, 144, 113, 40, 174, 169, 172, 57, 128, 65, 47, 98, 84, 127, 119, 5, 2, 63, 148, 16, 74, 130, 0, 123, 32, 132, 179, 25, 170, 23, 50, 164, 45, 166, 58, 17, 97, 104, 177, 81, 35, 20, 154, 138, 28, 118, 105, 11, 33, 53, 41, 176, 175, 167, 42, 91, 87, 150, 43, 153, 60, 162, 19, 101, 137, 27, 70, 78, 158, 49, 80, 136, 62, 103, 92, 124, 15, 147, 115, 90, 56, 142, 64, 52, 79, 120, 109, 126, 24, 51, 26, 66, 61, 44, 107, 3, 37, 54, 31, 72, 69, 10, 83, 122, 168, 36, 21, 13, 129, 155, 143, 111, 96, 82, 141, 12, 18, 1, 55, 34, 38, 116, 178, 4, 30, 131, 100, 9, 161, 121, 151, 160, 165, 48, 108, 173, 117, 85, 133, 157, 95, 6, 8, 102, 71, 77, 39, 156, 67, 110, 93, 14, 99, 46, 145, 125, 75, 76, 140, 134, 171, 94, and 159.

FIG. 295 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 6/15.

According to the original GW pattern (A) of FIG. 295, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 66, 21, 51, 55, 117, 24, 33, 12, 70, 63, 47, 65, 145, 8, 0, 57, 23, 71, 59, 14, 40, 42, 15, 56, 2, 43, 64, 58, 67, 53, 68, 61, 39, 52, 69, 1, 22, 31, 161, 38, 30, 19, 17, 18, 4, 41, 25, 44, 136, 29, 36, 26, 126, 177, 62, 37, 148, 9, 13, 45, 46, 152, 50, 49, 27, 77, 60, 35, 48, 178, 28, 34, 106, 127, 76, 131, 105, 138, 75, 130, 101, 167, 54, 173, 113, 108, 92, 135, 124, 121, 97, 149, 143, 81, 32, 96, 3, 78, 107, 86, 98, 16, 162, 150, 111, 158, 172, 139, 74, 142, 166, 7, 5, 119, 20, 144, 151, 90, 11, 156, 100, 175, 83, 155, 159, 128, 88, 87, 93, 103, 94, 140, 165, 6, 137, 157, 10, 85, 141, 129, 146, 122, 73, 112, 132, 125, 174, 169, 168, 79, 84, 118, 179, 147, 91, 160, 163, 115, 89, 80, 102, 104, 134, 82, 95, 133, 164, 154, 120, 110, 170, 114, 153, 72, 109, 171, 176, 99, 116, and 123.

According to the converted GW pattern (B) of FIG. 295, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 66, 57, 68, 41, 46, 131, 97, 158, 100, 157, 84, 133, 21, 23, 61, 25, 152, 105, 149, 172, 175, 10, 118, 164, 51, 71, 39, 44, 50, 138, 143, 139, 83, 85, 179, 154, 55, 59, 52, 136, 49, 75, 81, 74, 155, 141, 147, 120, 117, 14, 69, 29, 27, 130, 32, 142, 159, 129, 91, 110, 24, 40, 1, 36, 77, 101, 96, 166, 128, 146, 160, 170, 33, 42, 22, 26, 60, 167, 3, 7, 88, 122, 163, 114, 12, 15, 31, 126, 35, 54, 78, 5, 87, 73, 115, 153, 70, 56, 161, 177, 48, 173, 107, 119, 93, 112, 89, 72, 63, 2, 38, 62, 178, 113, 86, 20, 103, 132, 80, 109, 47, 43, 30, 37, 28, 108, 98, 144, 94, 125, 102, 171, 65, 64, 19, 148, 34, 92, 16, 151, 140, 174, 104, 176, 145, 58, 17, 9, 106, 135, 162, 90, 165, 169, 134, 99, 8, 67, 18, 13, 127, 124, 150, 11, 6, 168, 82, 116, 0, 53, 4, 45, 76, 121, 111, 156, 137, 79, 95, and 123.

FIG. 296 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 7/15.

According to the original GW pattern (A) of FIG. 296, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 59, 60, 0, 48, 87, 30, 29, 146, 142, 8, 150, 171, 20, 121, 23, 122, 144, 76, 162, 106, 50, 39, 63, 108, 165, 174, 16, 85, 58, 43, 161, 34, 13, 92, 79, 82, 175, 86, 69, 68, 15, 113, 84, 118, 27, 93, 120, 61, 73, 104, 10, 38, 45, 7, 173, 75, 24, 77, 137, 21, 37, 46, 3, 6, 168, 148, 109, 123, 103, 140, 64, 117, 158, 114, 136, 112, 31, 70, 134, 163, 98, 91, 33, 115, 95, 176, 154, 107, 97, 131, 111, 129, 40, 66, 170, 41, 74, 138, 99, 179, 81, 157, 32, 19, 26, 62, 172, 78, 160, 57, 22, 159, 51, 135, 2, 55, 164, 153, 155, 14, 42, 149, 127, 133, 83, 96, 139, 89, 36, 125, 130, 143, 147, 67, 18, 102, 94, 35, 101, 44, 49, 177, 88, 11, 105, 151, 12, 132, 25, 128, 119, 65, 145, 4, 54, 90, 71, 167, 166, 1, 156, 56, 124, 17, 141, 72, 9, 28, 5, 110, 100, 47, 80, 169, 116, 53, 152, 52, 126, and 178.

According to the converted GW pattern (B) of FIG. 296, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 59, 122, 161, 93, 37, 112, 111, 62, 42, 102, 119, 72, 60, 144, 34, 120, 46, 31, 129, 172, 149, 94, 65, 9, 0, 76, 13, 61, 3, 70, 40, 78, 127, 35, 145, 28, 48, 162, 92, 73, 6, 134, 66, 160, 133, 101, 4, 5, 87, 106, 79, 104, 168, 163, 170, 57, 83, 44, 54, 110, 30, 50, 82, 10, 148, 98, 41, 22, 96, 49, 90, 100, 29, 39, 175, 38, 109, 91, 74, 159, 139, 177, 71, 47, 146, 63, 86, 45, 123, 33, 138, 51, 89, 88, 167, 80, 142, 108, 69, 7, 103, 115, 99, 135, 36, 11, 166, 169, 8, 165, 68, 173, 140, 95, 179, 2, 125, 105, 1, 116, 150, 174, 15, 75, 64, 176, 81, 55, 130, 151, 156, 53, 171, 16, 113, 24, 117, 154, 157, 164, 143, 12, 56, 152, 20, 85, 84, 77, 158, 107, 32, 153, 147, 132, 124, 52, 121, 58, 118, 137, 114, 97, 19, 155, 67, 25, 17, 126, 23, 43, 27, 21, 136, 131, 26, 14, 18, 128, 141, and 178.

FIG. 297 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 297, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 48, 82, 51, 57, 69, 65, 6, 71, 90, 84, 81, 50, 88, 61, 55, 53, 73, 39, 13, 79, 75, 41, 18, 38, 89, 49, 93, 36, 64, 47, 40, 42, 76, 70, 56, 3, 72, 2, 54, 52, 145, 19, 78, 80, 63, 87, 67, 86, 10, 1, 58, 17, 14, 175, 91, 68, 85, 94, 15, 43, 74, 60, 66, 37, 92, 4, 9, 16, 83, 46, 44, 102, 30, 112, 122, 110, 29, 20, 105, 138, 101, 174, 33, 137, 136, 131, 166, 59, 34, 62, 125, 28, 26, 45, 24, 23, 21, 157, 98, 35, 95, 22, 32, 103, 27, 113, 31, 119, 173, 168, 118, 120, 114, 149, 159, 155, 179, 160, 161, 130, 123, 172, 139, 124, 153, 0, 109, 167, 128, 107, 117, 147, 177, 96, 164, 152, 11, 148, 158, 129, 163, 176, 151, 171, 8, 106, 144, 150, 169, 108, 162, 143, 111, 141, 133, 178, 134, 146, 99, 132, 142, 104, 115, 135, 121, 100, 12, 170, 156, 126, 5, 127, 154, 97, 140, 116, 165, 7, and 25.

According to the converted GW pattern (B) of FIG. 297, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 55, 47, 63, 43, 122, 62, 27, 130, 164, 108, 121, 48, 53, 40, 87, 74, 110, 125, 113, 123, 152, 162, 100, 82, 73, 42, 67, 60, 29, 28, 31, 172, 11, 143, 12, 51, 39, 76, 86, 66, 20, 26, 119, 139, 148, 111, 170, 57, 13, 70, 10, 37, 105, 45, 173, 124, 158, 141, 156, 69, 79, 56, 1, 92, 138, 24, 168, 153, 129, 133, 126, 65, 75, 3, 58, 4, 101, 23, 118, 0, 163, 178, 5, 6, 41, 72, 17, 9, 174, 21, 120, 109, 176, 134, 127, 71, 18, 2, 14, 16, 33, 157, 114, 167, 151, 146, 154, 90, 38, 54, 175, 83, 137, 98, 149, 128, 171, 99, 97, 84, 89, 52, 91, 46, 136, 35, 159, 107, 8, 132, 140, 81, 49, 145, 68, 44, 131, 95, 155, 117, 106, 142, 116, 50, 93, 19, 85, 102, 166, 22, 179, 147, 144, 104, 165, 88, 36, 78, 94, 30, 59, 32, 160, 177, 150, 115, 7, 61, 64, 80, 15, 112, 34, 103, 161, 96, 169, 135, and 25.

FIG. 298 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 9/15.

According to the original GW pattern (A) of FIG. 298, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 67, 79, 72, 175, 1, 92, 63, 65, 36, 73, 18, 3, 43, 78, 5, 40, 82, 20, 15, 76, 28, 84, 59, 91, 93, 54, 58, 60, 2, 19, 66, 44, 85, 48, 0, 50, 166, 89, 41, 24, 83, 75, 55, 64, 52, 98, 39, 141, 34, 74, 33, 45, 99, 46, 10, 69, 94, 101, 56, 9, 97, 96, 37, 14, 31, 70, 106, 113, 80, 62, 100, 13, 32, 88, 57, 127, 53, 68, 146, 61, 7, 107, 71, 51, 161, 81, 49, 86, 95, 103, 30, 25, 126, 87, 22, 47, 27, 171, 102, 6, 132, 77, 90, 38, 167, 4, 35, 26, 118, 140, 104, 128, 179, 124, 109, 159, 42, 110, 21, 105, 148, 142, 134, 23, 117, 122, 160, 12, 154, 114, 156, 151, 145, 169, 11, 139, 177, 129, 155, 178, 138, 176, 147, 121, 136, 165, 170, 133, 149, 150, 174, 168, 125, 116, 115, 164, 29, 119, 153, 157, 162, 173, 112, 144, 172, 123, 137, 16, 120, 131, 111, 135, 163, 17, 130, 152, 108, 8, 158, and 143.

According to the converted GW pattern (B) of FIG. 298, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 67, 40, 66, 98, 97, 127, 30, 4, 148, 139, 174, 123, 79, 82, 44, 39, 96, 53, 25, 35, 142, 177, 168, 137, 72, 20, 85, 141, 37, 68, 126, 26, 134, 129, 125, 16, 175, 15, 48, 34, 14, 146, 87, 118, 23, 155, 116, 120, 1, 76, 0, 74, 31, 61, 22, 140, 117, 178, 115, 131, 92, 28, 50, 33, 70, 7, 47, 104, 122, 138, 164, 111, 63, 84, 166, 45, 106, 107, 27, 128, 160, 176, 29, 135, 65, 59, 89, 99, 113, 71, 171, 179, 12, 147, 119, 163, 36, 91, 41, 46, 80, 51, 102, 124, 154, 121, 153, 17, 73, 93, 24, 10, 62, 161, 6, 109, 114, 136, 157, 130, 18, 54, 83, 69, 100, 81, 132, 159, 156, 165, 162, 152, 3, 58, 75, 94, 13, 49, 77, 42, 151, 170, 173, 108, 43, 60, 55, 101, 32, 86, 90, 110, 145, 133, 112, 8, 78, 2, 64, 56, 88, 95, 38, 21, 169, 149, 144, 158, 5, 19, 52, 9, 57, 103, 167, 105, 11, 150, 172, and 143.

FIG. 299 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 299, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 36, 21, 117, 71, 38, 108, 42, 61, 13, 88, 97, 68, 2, 67, 50, 64, 95, 63, 100, 9, 82, 51, 45, 78, 31, 18, 103, 39, 119, 25, 40, 28, 72, 11, 73, 86, 131, 84, 111, 24, 58, 60, 81, 37, 89, 1, 93, 56, 69, 96, 35, 57, 116, 130, 55, 74, 41, 169, 54, 14, 26, 65, 83, 165, 107, 0, 52, 144, 75, 101, 8, 115, 118, 85, 48, 112, 80, 90, 32, 173, 76, 33, 16, 77, 164, 104, 46, 20, 98, 109, 29, 114, 7, 110, 99, 53, 133, 70, 87, 106, 145, 4, 113, 27, 59, 34, 5, 102, 148, 142, 79, 19, 44, 159, 174, 155, 136, 94, 43, 49, 152, 161, 66, 3, 121, 135, 147, 17, 157, 30, 153, 154, 137, 168, 92, 149, 171, 10, 177, 134, 143, 176, 179, 105, 172, 47, 146, 160, 23, 175, 141, 91, 140, 163, 132, 6, 126, 124, 12, 170, 167, 151, 125, 139, 150, 15, 129, 162, 120, 166, 156, 62, 158, 178, 128, 127, 22, 122, 123, and 138.

According to the converted GW pattern (B) of FIG. 299, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 36, 64, 40, 1, 26, 112, 29, 34, 152, 149, 141, 15, 21, 95, 28, 93, 65, 80, 114, 5, 161, 171, 91, 129, 117, 63, 72, 56, 83, 90, 7, 102, 66, 10, 140, 162, 71, 100, 11, 69, 165, 32, 110, 148, 3, 177, 163, 120, 38, 9, 73, 96, 107, 173, 99, 142, 121, 134, 132, 166, 108, 82, 86, 35, 0, 76, 53, 79, 135, 143, 6, 156, 42, 51, 131, 57, 52, 33, 133, 19, 147, 176, 126, 62, 61, 45, 84, 116, 144, 16, 70, 44, 17, 179, 124, 158, 13, 78, 111, 130, 75, 77, 87, 159, 157, 105, 12, 178, 88, 31, 24, 55, 101, 164, 106, 174, 30, 172, 170, 128, 97, 18, 58, 74, 8, 104, 145, 155, 153, 47, 167, 127, 68, 103, 60, 41, 115, 46, 4, 136, 154, 146, 151, 22, 2, 39, 81, 169, 118, 20, 113, 94, 137, 160, 125, 122, 67, 119, 37, 54, 85, 98, 27, 43, 168, 23, 139, 123, 50, 25, 89, 14, 48, 109, 59, 49, 92, 175, 150, and 138.

FIG. 300 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 11/15.

According to the original GW pattern (A) of FIG. 300, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 97, 3, 44, 119, 72, 83, 116, 40, 0, 111, 8, 68, 43, 24, 102, 49, 92, 65, 31, 93, 60, 17, 76, 89, 118, 70, 87, 15, 67, 22, 59, 95, 46, 38, 125, 48, 58, 140, 104, 73, 47, 14, 120, 1, 50, 80, 63, 62, 45, 9, 25, 114, 19, 82, 54, 150, 121, 130, 123, 37, 55, 23, 98, 81, 122, 103, 85, 126, 101, 78, 5, 128, 148, 57, 12, 107, 36, 2, 109, 52, 39, 66, 115, 42, 156, 90, 51, 91, 29, 84, 18, 144, 10, 94, 64, 100, 86, 71, 27, 30, 32, 110, 33, 113, 131, 35, 34, 112, 26, 108, 16, 61, 56, 75, 41, 117, 69, 172, 96, 149, 127, 124, 173, 13, 74, 105, 53, 161, 146, 174, 79, 88, 28, 129, 134, 139, 136, 145, 170, 135, 158, 154, 162, 7, 169, 99, 106, 137, 165, 143, 4, 175, 138, 133, 171, 168, 147, 167, 141, 163, 176, 179, 142, 11, 177, 153, 151, 159, 132, 20, 164, 6, 157, 178, 21, 166, 155, 160, and 152.

According to the converted GW pattern (B) of FIG. 300, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 77, 102, 22, 50, 37, 12, 84, 131, 149, 134, 143, 177, 97, 49, 59, 80, 55, 107, 18, 35, 127, 139, 4, 153, 3, 92, 95, 63, 23, 36, 144, 34, 124, 136, 175, 151, 44, 65, 46, 62, 98, 2, 10, 112, 173, 145, 138, 159, 119, 31, 38, 45, 81, 109, 94, 26, 13, 170, 133, 132, 72, 93, 125, 9, 122, 52, 64, 108, 74, 135, 171, 20, 83, 60, 48, 25, 103, 39, 100, 16, 105, 158, 168, 164, 116, 17, 58, 114, 85, 66, 86, 61, 53, 154, 147, 6, 40, 76, 140, 19, 126, 115, 71, 56, 161, 162, 167, 157, 0, 89, 104, 82, 101, 42, 27, 75, 146, 7, 141, 178, 111, 118, 73, 54, 78, 156, 30, 41, 174, 169, 163, 21, 8, 70, 47, 150, 5, 90, 32, 117, 79, 99, 176, 166, 68, 87, 14, 121, 128, 51, 110, 69, 88, 106, 179, 155, 43, 15, 120, 130, 148, 91, 33, 172, 28, 137, 142, 160, 24, 67, 1, 123, 57, 29, 113, 96, 129, 165, 11, and 152.

FIG. 301 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 301, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 110, 16, 64, 100, 55, 70, 48, 26, 60, 71, 93, 1, 59, 88, 97, 136, 67, 94, 90, 72, 49, 23, 41, 92, 9, 35, 37, 113, 101, 111, 8, 52, 56, 19, 134, 151, 84, 126, 159, 63, 44, 65, 139, 31, 57, 103, 22, 116, 172, 38, 95, 36, 46, 141, 114, 4, 106, 149, 85, 86, 66, 51, 121, 105, 109, 87, 6, 135, 127, 47, 123, 39, 10, 148, 43, 131, 147, 45, 143, 5, 108, 81, 2, 140, 120, 132, 76, 58, 137, 18, 29, 125, 17, 30, 32, 156, 133, 78, 91, 161, 104, 174, 53, 61, 50, 74, 77, 33, 171, 138, 28, 69, 112, 119, 12, 102, 20, 167, 99, 122, 117, 24, 98, 115, 124, 42, 7, 79, 75, 128, 82, 68, 80, 3, 11, 54, 96, 40, 129, 142, 107, 73, 175, 14, 83, 150, 165, 118, 89, 130, 15, 163, 34, 166, 173, 146, 168, 153, 154, 177, 62, 145, 0, 178, 155, 157, 179, 144, 158, 152, 13, 25, 176, 162, 169, 164, 27, 21, 160, and 170.

According to the converted GW pattern (B) of FIG. 301, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 110, 136, 8, 103, 66, 131, 29, 74, 117, 54, 15, 157, 16, 67, 52, 22, 51, 147, 125, 77, 24, 96, 163, 179, 64, 94, 56, 116, 121, 45, 17, 33, 98, 40, 34, 144, 100, 90, 19, 172, 105, 143, 30, 171, 115, 129, 166, 158, 55, 72, 134, 38, 109, 5, 32, 138, 124, 142, 173, 152, 70, 49, 151, 95, 87, 108, 156, 28, 42, 107, 146, 13, 48, 23, 84, 36, 6, 81, 133, 69, 7, 73, 168, 25, 26, 41, 126, 46, 135, 2, 78, 112, 79, 175, 153, 176, 60, 92, 159, 141, 127, 140, 91, 119, 75, 14, 154, 162, 71, 9, 63, 114, 47, 120, 161, 12, 128, 83, 177, 169, 93, 35, 44, 4, 123, 132, 104, 102, 82, 150, 62, 164, 1, 37, 65, 106, 39, 76, 174, 20, 68, 165, 145, 27, 59, 113, 139, 149, 10, 58, 53, 167, 80, 118, 0, 21, 88, 101, 31, 85, 148, 137, 61, 99, 3, 89, 178, 160, 97, 111, 57, 86, 43, 18, 50, 122, 11, 130, 155, and 170.

FIG. 302 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 302, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 87, 50, 6, 42, 82, 54, 96, 0, 62, 124, 109, 126, 23, 64, 53, 20, 41, 111, 145, 135, 68, 2, 122, 128, 107, 7, 28, 14, 125, 136, 154, 10, 92, 99, 84, 86, 151, 108, 24, 94, 148, 29, 123, 13, 88, 52, 35, 61, 102, 132, 95, 70, 40, 129, 101, 36, 51, 150, 142, 152, 121, 131, 116, 97, 104, 31, 59, 137, 83, 112, 113, 57, 77, 32, 93, 49, 58, 117, 78, 1, 149, 37, 11, 100, 85, 79, 72, 66, 130, 18, 63, 55, 91, 46, 146, 21, 143, 44, 110, 75, 138, 16, 76, 45, 114, 144, 119, 38, 140, 65, 30, 133, 153, 33, 89, 71, 115, 105, 90, 56, 25, 103, 147, 73, 60, 47, 118, 27, 69, 9, 74, 48, 19, 39, 43, 34, 81, 139, 3, 164, 106, 134, 5, 67, 80, 141, 120, 98, 155, 8, 156, 162, 163, 165, 26, 161, 168, 176, 159, 170, 4, 127, 22, 173, 157, 171, 178, 158, 17, 174, 179, 167, 12, 172, 166, 160, 177, 169, 175, and 15.

According to the converted GW pattern (B) of FIG. 302, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 87, 20, 154, 52, 121, 49, 63, 144, 25, 34, 156, 171, 50, 41, 10, 35, 131, 58, 55, 119, 103, 81, 162, 178, 6, 111, 92, 61, 116, 117, 91, 38, 147, 139, 163, 158, 42, 145, 99, 102, 97, 78, 46, 140, 73, 3, 165, 17, 82, 135, 84, 132, 104, 1, 146, 65, 60, 164, 26, 174, 54, 68, 86, 95, 31, 149, 21, 30, 47, 106, 161, 179, 96, 2, 151, 70, 59, 37, 143, 133, 118, 134, 168, 167, 0, 122, 108, 40, 137, 11, 44, 153, 27, 5, 176, 12, 62, 128, 24, 129, 83, 100, 110, 33, 69, 67, 159, 172, 124, 107, 94, 101, 112, 85, 75, 89, 9, 80, 170, 166, 109, 7, 148, 36, 113, 79, 138, 71, 74, 141, 4, 160, 126, 28, 29, 51, 57, 72, 16, 115, 48, 120, 127, 177, 23, 14, 123, 150, 77, 66, 76, 105, 19, 98, 22, 169, 64, 125, 13, 142, 32, 130, 45, 90, 39, 155, 173, 175, 53, 136, 88, 152, 93, 18, 114, 56, 43, 8, 157, and 15.

Example of GW Pattern Set to MODCOD (LDPC Code of 16 k Bits)

FIG. 303 shows an example of the GW pattern set to the MODCOD which is the combination of the modulation scheme and the LDPC code of 16 k bits.

Similarly to FIG. 230, in FIG. 303, a case where “A”s are described in the MODCODs which are combinations of 4 types of modulation schemes (MODs) and code rates (CR) of 12 types of LDPC codes means that it is assumed that the block interleaving of the type A is performed, and the GW patterns for the block interleaving of the type A are set. A case where “B”s are described means that it is assumed that the block interleaving of the type B is performed, and the GW patterns for the block interleaving of the type B are set.

In FIG. 303, in the MODCODs in which the modulation scheme is QPSK (MOD 2) and the code rates r of the LDPC code of 16 k bits are 2/15, 3/15, 4/15, 5/15, 8/15, 10/15, 11/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is QPSK (MOD 2) and the code rates r of the LDPC code of 16 k bits are 6/15, 7/15, and 9/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 303, in the MODCODs in which the modulation scheme is 16-QAM (MOD 4) and the code rates r of the LDPC code of 16 k bits are 2/15, 3/15, 4/15, 5/15, 8/15, 10/15, and 12/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 16-QAM (MOD 4) and the code rates r of the LDPC code of 16 k bits are 6/15, 7/15, 9/15, 11/15, and 13/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 303, in the MODCODs in which the modulation scheme is 64-QAM (MOD 6) and the code rates r of the LDPC code of 16 k bits are 2/15, 3/15, 4/15, 5/15, 8/15, 10/15, 11/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 64-QAM (MOD 6) and the code rates r of the LDPC code of 16 k bits are 6/15, 7/15, and 9/15, it is assumed that the block interleaving of the type B is performed.

In FIG. 303, in the MODCODs in which the modulation scheme is 256-QAM (MOD 8) and the code rates r of the LDPC code of 16 k bits are 2/15, 3/15, 4/15, 5/15, 7/15, 8/15, 9/15, 10/15, 12/15, and 13/15, it is assumed that the block interleaving of the type A is performed. Meanwhile, in the MODCODs in which the modulation scheme is 256-QAM (MOD 8) and the code rates r of the LDPC code of 16 k bits are 6/15, and 11/15, it is assumed that the block interleaving of the type B is performed.

As stated above, the GW pattern for the block interleaving of the type A or the GW pattern for the block interleaving of the type B is set to each MODCOD which is the combination of the modulation scheme and the LDPC code of 16 k bits depending on the assumed type A.

As mentioned above, when it is assumed that the block interleaving of the type B is performed in the group-wise interleaver 1021, the GW pattern for the block interleaving of the type B is rewritten into the GW pattern for the block interleaving of the type A such that a block interleaving effect obtained when the block interleaving of the type A is performed is the same as a block interleaving effect obtained when the block interleaving of the type B is performed.

When it is assumed that the block interleaving of the type A is performed in the group-wise interleaver 1021, the GW pattern for the block interleaving of the type A is rewritten into the GW pattern for the block interleaving of the type B such that a block interleaving effect obtained when the block interleaving of the type B is performed is the same as a block interleaving effect obtained when the block interleaving of the type A is performed.

As a specific example of the GW pattern set to each MODCOD shown in FIG. 303, an original GW pattern and a converted GW pattern will be described. The UC or NUC may be applied to the QAM constellation such as 16-QAM.

In each MODCOD, when the GW pattern for the block interleaving of the type A is set as an original GW pattern (A), the GW pattern for the block interleaving of the type B is set as a converted GW pattern (B). By contrast, when the GW pattern for the block interleaving of the type B is set as an original GW pattern (B), the GW pattern for the block interleaving of the type A is set as a converted GW pattern (A).

FIG. 304 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 304, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 304, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 305 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 305, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 15, 22, 34, 19, 7, 17, 28, 43, 30, 32, 14, 1, 11, 0, 3, 9, 10, 38, 24, 4, 23, 18, 27, 39, 29, 33, 8, 2, 40, 21, 20, 36, 44, 12, 37, 13, 35, 6, 31, 26, 16, 25, 42, 5, and 41.

According to the converted GW pattern (B) of FIG. 305, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 15, 27, 22, 39, 34, 29, 19, 33, 7, 8, 17, 2, 28, 40, 43, 21, 30, 20, 32, 36, 14, 44, 1, 12, 11, 37, 0, 13, 3, 35, 9, 6, 10, 31, 38, 26, 24, 16, 4, 25, 23, 42, 18, 5, and 41.

FIG. 306 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 306, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 306, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 307 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 307, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 35, 7, 29, 11, 14, 32, 38, 28, 20, 17, 25, 39, 19, 4, 1, 12, 10, 30, 0, 44, 43, 2, 21, 5, 13, 34, 37, 23, 15, 36, 18, 42, 16, 33, 31, 27, 22, 3, 6, 40, 24, 41, 9, 26, and 8.

According to the converted GW pattern (B) of FIG. 307, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 35, 21, 7, 5, 29, 13, 11, 34, 14, 37, 32, 23, 38, 15, 28, 36, 20, 18, 17, 42, 25, 16, 39, 33, 19, 31, 4, 27, 1, 22, 12, 3, 10, 6, 30, 40, 0, 24, 44, 41, 43, 9, 2, 26, and 8.

FIG. 308 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 6/15.

According to the original GW pattern (B) of FIG. 308, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 7, 4, 0, 5, 27, 30, 25, 13, 31, 9, 34, 10, 17, 11, 8, 12, 15, 16, 18, 19, 20, 21, 22, 23, 1, 35, 24, 29, 33, 6, 26, 14, 32, 28, 2, 3, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 308, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 7, 0, 27, 25, 31, 34, 17, 8, 15, 18, 20, 22, 1, 24, 33, 26, 32, 2, 36, 38, 40, 42, 4, 5, 30, 13, 9, 10, 11, 12, 16, 19, 21, 23, 35, 29, 6, 14, 28, 3, 37, 39, 41, 43, and 44.

FIG. 309 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 309, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 7, 1, 4, 18, 21, 22, 6, 9, 5, 17, 14, 13, 15, 10, 20, 8, 19, 16, 12, 0, 11, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 309, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 1, 18, 22, 9, 17, 13, 10, 8, 16, 0, 2, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 7, 4, 21, 6, 5, 14, 15, 20, 19, 12, 11, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

FIG. 310 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 310, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 310, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 311 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 311, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 311, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

FIG. 312 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 312, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 1, 4, 5, 6, 24, 21, 18, 7, 17, 12, 8, 20, 23, 29, 28, 30, 32, 34, 36, 38, 40, 42, 0, 2, 3, 14, 22, 13, 10, 25, 9, 27, 19, 16, 15, 26, 11, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 312, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 1, 0, 4, 2, 5, 3, 6, 14, 24, 22, 21, 13, 18, 10, 7, 25, 17, 9, 12, 27, 8, 19, 20, 16, 23, 15, 29, 26, 28, 11, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 313 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 11/15.

According to the original GW pattern (A) of FIG. 313, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 313, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 314 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 314, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, and 44.

According to the converted GW pattern (B) of FIG. 314, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

FIG. 315 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 315, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 26, 10, 12, 38, 28, 15, 0, 44, 34, 24, 14, 8, 40, 30, 20, 13, 42, 32, 22, 11, 9, 36, 25, 7, 5, 37, 27, 4, 16, 43, 33, 23, 2, 18, 39, 29, 19, 6, 41, 31, 21, 3, 17, 35, and 1.

According to the converted GW pattern (B) of FIG. 315, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 26, 25, 10, 7, 12, 5, 38, 37, 28, 27, 15, 4, 0, 16, 44, 43, 34, 33, 24, 23, 14, 2, 8, 18, 40, 39, 30, 29, 20, 19, 13, 6, 42, 41, 32, 31, 22, 21, 11, 3, 9, 17, 36, 35, and 1.

FIG. 316 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 316, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 33, 18, 8, 29, 10, 21, 14, 30, 26, 11, 23, 27, 4, 7, 6, 24, 44, 38, 31, 34, 43, 13, 0, 15, 42, 17, 2, 20, 12, 40, 39, 35, 32, 1, 3, 41, 37, 9, 25, 19, 22, 16, 28, and 36.

According to the converted GW pattern (B) of FIG. 316, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 23, 13, 32, 33, 27, 0, 1, 18, 4, 15, 3, 8, 7, 42, 41, 29, 6, 17, 37, 10, 24, 2, 9, 21, 44, 20, 25, 14, 38, 12, 19, 30, 31, 40, 22, 26, 34, 39, 16, 11, 43, 35, 28, and 36.

FIG. 317 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 317, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 18, 16, 5, 29, 26, 43, 23, 6, 1, 24, 7, 19, 37, 2, 27, 3, 10, 15, 36, 39, 22, 12, 35, 33, 4, 17, 30, 31, 21, 9, 11, 41, 0, 32, 20, 40, 25, 8, 34, 38, 28, 14, 44, 13, and 42.

According to the converted GW pattern (B) of FIG. 317, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 18, 19, 35, 32, 16, 37, 33, 20, 5, 2, 4, 40, 29, 27, 17, 25, 26, 3, 30, 8, 43, 10, 31, 34, 23, 15, 21, 38, 6, 36, 9, 28, 1, 39, 11, 14, 24, 22, 41, 44, 7, 12, 0, 13, and 42.

FIG. 318 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 318, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 34, 3, 19, 35, 25, 2, 17, 36, 26, 38, 0, 40, 27, 10, 7, 43, 21, 28, 15, 6, 1, 37, 18, 30, 32, 33, 29, 22, 12, 13, 5, 23, 44, 14, 4, 31, 20, 39, 42, 11, 9, 16, 41, 8, and 24.

According to the converted GW pattern (B) of FIG. 318, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 34, 40, 18, 14, 3, 27, 30, 4, 19, 10, 32, 31, 35, 7, 33, 20, 25, 43, 29, 39, 2, 21, 22, 42, 17, 28, 12, 11, 36, 15, 13, 9, 26, 6, 5, 16, 38, 1, 23, 41, 0, 37, 44, 8, and 24.

FIG. 319 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 319, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 33, 39, 2, 38, 29, 0, 10, 25, 17, 7, 21, 44, 37, 8, 34, 20, 1, 4, 31, 11, 42, 22, 13, 12, 28, 26, 43, 30, 14, 16, 23, 24, 15, 5, 18, 9, 36, 6, 19, 32, 40, 41, 35, and 27.

According to the converted GW pattern (B) of FIG. 319, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 21, 22, 15, 33, 44, 13, 5, 39, 37, 12, 18, 2, 8, 28, 9, 38, 34, 26, 36, 29, 20, 43, 6, 0, 1, 30, 19, 10, 4, 14, 32, 25, 31, 16, 40, 17, 11, 23, 41, 7, 42, 24, 35, and 27.

FIG. 320 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 6/15.

According to the original GW pattern (B) of FIG. 320, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 12, 13, 15, 30, 27, 25, 11, 34, 9, 4, 31, 22, 6, 32, 7, 21, 17, 3, 1, 26, 10, 33, 19, 2, 18, 5, 28, 35, 8, 16, 29, 23, 14, 0, 20, 24, 36, 37, 38, 39, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 320, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 12, 27, 9, 6, 17, 10, 18, 8, 14, 36, 40, 13, 25, 4, 32, 3, 33, 5, 16, 0, 37, 41, 15, 11, 31, 7, 1, 19, 28, 29, 20, 38, 42, 30, 34, 22, 21, 26, 2, 35, 23, 24, 39, 43, and 44.

FIG. 321 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 321, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 19, 3, 32, 38, 16, 17, 29, 33, 14, 10, 6, 2, 20, 15, 40, 39, 12, 22, 23, 34, 31, 13, 44, 43, 36, 24, 37, 42, 0, 9, 4, 21, 5, 35, 26, 41, 7, 28, 11, 25, 8, 18, 1, 30, and 27.

According to the converted GW pattern (A) of FIG. 321, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 19, 16, 14, 20, 12, 31, 36, 0, 5, 7, 8, 3, 17, 10, 15, 22, 13, 24, 9, 35, 28, 18, 32, 29, 6, 40, 23, 44, 37, 4, 26, 11, 1, 38, 33, 2, 39, 34, 43, 42, 21, 41, 25, 30, and 27.

FIG. 322 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 322, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 36, 5, 22, 26, 1, 13, 3, 33, 9, 6, 23, 20, 35, 10, 17, 41, 30, 15, 21, 42, 29, 11, 37, 4, 2, 38, 44, 0, 18, 19, 8, 31, 28, 43, 14, 34, 32, 25, 40, 12, 16, 24, 39, 27, and 7.

According to the converted GW pattern (B) of FIG. 322, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 36, 20, 37, 43, 5, 35, 4, 14, 22, 10, 2, 34, 26, 17, 38, 32, 1, 41, 44, 25, 13, 30, 0, 40, 3, 15, 18, 12, 33, 21, 19, 16, 9, 42, 8, 24, 6, 29, 31, 39, 23, 11, 28, 27, and 7.

FIG. 323 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 323, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 4, 6, 19, 2, 5, 30, 20, 11, 22, 12, 15, 0, 36, 37, 38, 39, 26, 14, 34, 35, 16, 13, 18, 42, 7, 10, 25, 43, 40, 17, 41, 24, 33, 31, 23, 32, 21, 3, 27, 28, 8, 9, 29, 1, and 44.

According to the converted GW pattern (A) of FIG. 323, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 4, 5, 22, 36, 26, 16, 7, 40, 33, 21, 8, 6, 30, 12, 37, 14, 13, 10, 17, 31, 3, 9, 19, 20, 15, 38, 34, 18, 25, 41, 23, 27, 29, 2, 11, 0, 39, 35, 42, 43, 24, 32, 28, 1, and 44.

FIG. 324 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 324, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 27, 11, 20, 1, 7, 5, 29, 35, 9, 10, 34, 18, 25, 28, 6, 13, 17, 0, 23, 16, 41, 15, 19, 44, 24, 37, 4, 31, 8, 32, 14, 42, 12, 2, 40, 30, 36, 39, 43, 21, 3, 22, 26, 33, and 38.

According to the converted GW pattern (B) of FIG. 324, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 27, 18, 19, 2, 11, 25, 44, 40, 20, 28, 24, 30, 1, 6, 37, 36, 7, 13, 4, 39, 5, 17, 31, 43, 29, 0, 8, 21, 35, 23, 32, 3, 9, 16, 14, 22, 10, 41, 42, 26, 34, 15, 12, 33, and 38.

FIG. 325 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 11/15.

According to the original GW pattern (B) of FIG. 325, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 2, 4, 41, 8, 13, 7, 0, 24, 3, 22, 5, 32, 10, 9, 36, 37, 29, 11, 25, 16, 20, 21, 35, 34, 15, 1, 6, 14, 27, 30, 33, 12, 17, 28, 23, 40, 26, 31, 38, 39, 18, 19, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 325, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 2, 13, 3, 10, 29, 20, 15, 27, 17, 26, 18, 4, 7, 22, 9, 11, 21, 1, 30, 28, 31, 19, 41, 0, 5, 36, 25, 35, 6, 33, 23, 38, 42, 8, 24, 32, 37, 16, 34, 14, 12, 40, 39, 43, and 44.

FIG. 326 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 326, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 6, 7, 27, 2, 23, 10, 30, 22, 28, 24, 20, 37, 21, 4, 14, 11, 42, 16, 9, 15, 26, 33, 40, 5, 8, 44, 34, 18, 0, 32, 29, 19, 41, 38, 17, 25, 43, 35, 36, 13, 39, 12, 1, and 31.

According to the converted GW pattern (B) of FIG. 326, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 3, 20, 33, 41, 6, 37, 40, 38, 7, 21, 5, 17, 27, 4, 8, 25, 2, 14, 44, 43, 23, 11, 34, 35, 10, 42, 18, 36, 30, 16, 0, 13, 22, 9, 32, 39, 28, 15, 29, 12, 24, 26, 19, 1, and 31.

FIG. 327 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM and the code rate r is 13/15.

According to the original GW pattern (B) of FIG. 327, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 12, 7, 20, 43, 29, 13, 32, 30, 25, 0, 17, 18, 9, 1, 41, 42, 6, 33, 28, 14, 16, 11, 39, 40, 15, 4, 23, 5, 2, 24, 22, 38, 10, 8, 19, 34, 26, 36, 37, 27, 21, 31, 3, 35, and 44.

According to the converted GW pattern (A) of FIG. 327, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 12, 29, 25, 9, 6, 16, 15, 2, 10, 26, 21, 7, 13, 0, 1, 33, 11, 4, 24, 8, 36, 31, 20, 32, 17, 41, 28, 39, 23, 22, 19, 37, 3, 43, 30, 18, 42, 14, 40, 5, 38, 34, 27, 35, and 44.

FIG. 328 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 328, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 7, 11, 4, 38, 19, 25, 2, 43, 15, 26, 18, 14, 9, 29, 44, 32, 0, 5, 35, 10, 1, 12, 6, 36, 21, 33, 37, 34, 3, 31, 20, 16, 40, 23, 41, 22, 30, 39, 13, 24, 17, 42, 28, 8, and 27.

According to the converted GW pattern (B) of FIG. 328, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 7, 43, 44, 12, 3, 22, 11, 15, 32, 6, 31, 30, 4, 26, 0, 36, 20, 39, 38, 18, 5, 21, 16, 13, 19, 14, 35, 33, 40, 24, 25, 9, 10, 37, 23, 17, 2, 29, 1, 34, 41, 42, 28, 8, and 27.

FIG. 329 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 329, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 19, 34, 22, 6, 29, 25, 23, 36, 7, 8, 24, 16, 27, 43, 11, 35, 5, 28, 13, 4, 3, 17, 15, 38, 20, 0, 26, 12, 1, 39, 31, 41, 44, 30, 9, 21, 42, 18, 14, 32, 10, 2, 37, 33, and 40.

According to the converted GW pattern (B) of FIG. 329, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 19, 36, 11, 17, 1, 21, 34, 7, 35, 15, 39, 42, 22, 8, 5, 38, 31, 18, 6, 24, 28, 20, 41, 14, 29, 16, 13, 0, 44, 32, 25, 27, 4, 26, 30, 10, 23, 43, 3, 12, 9, 2, 37, 33, and 40.

FIG. 330 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 330, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 41, 34, 32, 37, 5, 8, 13, 15, 30, 31, 22, 25, 42, 20, 23, 17, 1, 40, 44, 12, 6, 43, 7, 29, 33, 16, 11, 0, 35, 4, 14, 28, 21, 3, 24, 19, 18, 36, 10, 38, 26, 2, 39, 27, and 9.

According to the converted GW pattern (B) of FIG. 330, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 41, 15, 23, 43, 35, 19, 34, 30, 17, 7, 4, 18, 32, 31, 1, 29, 14, 36, 37, 22, 40, 33, 28, 10, 5, 25, 44, 16, 21, 38, 8, 42, 12, 11, 3, 26, 13, 20, 6, 0, 24, 2, 39, 27, and 9.

FIG. 331 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 331, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 25, 44, 8, 39, 37, 2, 11, 7, 0, 12, 4, 31, 33, 38, 43, 21, 26, 13, 28, 29, 1, 27, 18, 17, 34, 3, 42, 10, 19, 20, 32, 36, 40, 9, 41, 5, 35, 30, 22, 15, 16, 6, 24, 23, and 14.

According to the converted GW pattern (B) of FIG. 331, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 25, 7, 43, 27, 19, 5, 44, 0, 21, 18, 20, 35, 8, 12, 26, 17, 32, 30, 39, 4, 13, 34, 36, 22, 37, 31, 28, 3, 40, 15, 2, 33, 29, 42, 9, 16, 11, 38, 1, 10, 41, 6, 24, 23, 14.

FIG. 332 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 6/15.

According to the original GW pattern (B) of FIG. 332, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 12, 39, 32, 30, 24, 28, 15, 38, 23, 27, 41, 0, 6, 17, 37, 42, 20, 11, 4, 40, 2, 3, 26, 10, 7, 13, 25, 1, 18, 8, 5, 14, 36, 35, 33, 22, 9, 44, 16, 34, 19, 21, 29, and 43.

According to the converted GW pattern (A) of FIG. 332, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 28, 0, 11, 10, 8, 22, 12, 15, 6, 4, 7, 5, 9, 39, 38, 17, 40, 13, 14, 44, 32, 23, 37, 2, 25, 36, 16, 30, 27, 42, 3, 1, 35, 34, 24, 41, 20, 26, 18, 33, 19, 21, 29, and 43.

FIG. 333 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 7/15.

According to the original GW pattern (B) of FIG. 333, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 2, 14, 10, 0, 37, 42, 38, 40, 24, 29, 28, 35, 18, 16, 20, 27, 41, 30, 15, 19, 9, 43, 25, 3, 6, 7, 31, 32, 26, 36, 17, 1, 13, 5, 39, 33, 4, 8, 23, 22, 11, 34, 44, 12, and 21.

According to the converted GW pattern (A) of FIG. 333, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 2, 38, 18, 15, 6, 17, 4, 14, 40, 16, 19, 7, 1, 8, 10, 24, 20, 9, 31, 13, 23, 0, 29, 27, 43, 32, 5, 22, 37, 28, 41, 25, 26, 39, 11, 42, 35, 30, 3, 36, 33, 34, 44, 12, and 21.

FIG. 334 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 334, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 36, 6, 2, 20, 43, 17, 33, 22, 23, 25, 13, 0, 10, 7, 21, 1, 19, 26, 8, 14, 31, 35, 16, 5, 29, 40, 11, 9, 4, 34, 15, 42, 32, 28, 18, 37, 30, 39, 24, 41, 3, 38, 27, 12, and 44.

According to the converted GW pattern (B) of FIG. 334, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 36, 22, 21, 35, 4, 37, 6, 23, 1, 16, 34, 30, 2, 25, 19, 5, 15, 39, 20, 13, 26, 29, 42, 24, 43, 0, 8, 40, 32, 41, 17, 10, 14, 11, 28, 3, 33, 7, 31, 9, 18, 38, 27, 12, and 44.

FIG. 335 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 9/15.

According to the original GW pattern (B) of FIG. 335, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 21, 5, 43, 38, 40, 1, 3, 17, 11, 37, 10, 41, 9, 15, 25, 44, 14, 27, 7, 18, 20, 35, 16, 0, 6, 19, 8, 22, 29, 28, 34, 31, 33, 30, 32, 42, 13, 4, 24, 26, 36, 2, 23, 12, and 39.

According to the converted GW pattern (A) of FIG. 335, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 21, 3, 9, 7, 6, 34, 13, 5, 17, 15, 18, 19, 31, 4, 43, 11, 25, 20, 8, 33, 24, 38, 37, 44, 35, 22, 30, 26, 40, 10, 14, 16, 29, 32, 36, 1, 41, 27, 0, 28, 42, 2, 23, 12, and 39.

FIG. 336 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 336, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 14, 22, 18, 11, 28, 26, 2, 38, 10, 0, 5, 12, 24, 17, 29, 16, 39, 13, 23, 8, 25, 43, 34, 33, 27, 15, 7, 1, 9, 35, 40, 32, 30, 20, 36, 31, 21, 41, 44, 3, 42, 6, 19, 37, and 4.

According to the converted GW pattern (B) of FIG. 336, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 14, 38, 29, 43, 9, 31, 22, 10, 16, 34, 35, 21, 18, 0, 39, 33, 40, 41, 11, 5, 13, 27, 32, 44, 28, 12, 23, 15, 30, 3, 26, 24, 8, 7, 20, 42, 2, 17, 25, 1, 36, 6, 19, 37, and 4.

FIG. 337 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 11/15.

According to the original pattern (A) of FIG. 337, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 20, 21, 25, 4, 16, 9, 3, 17, 24, 5, 10, 12, 28, 6, 19, 8, 15, 13, 11, 29, 22, 27, 14, 23, 34, 26, 18, 42, 2, 37, 44, 39, 33, 35, 41, 0, 36, 7, 40, 38, 1, 30, 32, and 43.

According to the converted GW pattern (B) of FIG. 337, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 3, 6, 22, 42, 41, 20, 17, 19, 27, 2, 0, 21, 24, 8, 14, 37, 36, 25, 5, 15, 23, 44, 7, 4, 10, 13, 34, 39, 40, 16, 12, 11, 26, 33, 38, 9, 28, 29, 18, 35, 1, 30, 32, and 43.

FIG. 338 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 338, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 11, 14, 7, 31, 10, 2, 26, 0, 32, 29, 22, 33, 12, 20, 28, 27, 39, 37, 15, 4, 5, 8, 13, 38, 18, 23, 34, 24, 6, 1, 9, 16, 44, 21, 3, 36, 30, 40, 35, 43, 42, 25, 19, and 41.

According to the converted GW pattern (B) of FIG. 338, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 26, 20, 5, 24, 3, 11, 0, 28, 8, 6, 36, 14, 32, 27, 13, 1, 30, 7, 29, 39, 38, 9, 40, 31, 22, 37, 18, 16, 35, 10, 33, 15, 23, 44, 43, 2, 12, 4, 34, 21, 42, 25, 19, and 41.

FIG. 339 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 339, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 9, 7, 15, 10, 11, 12, 13, 6, 21, 17, 14, 20, 26, 8, 25, 32, 34, 23, 2, 4, 31, 18, 5, 27, 29, 3, 38, 36, 39, 43, 41, 42, 40, 44, 1, 28, 33, 22, 16, 19, 24, 0, 30, 35, and 37.

According to the converted GW pattern (B) of FIG. 339, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 9, 6, 25, 18, 39, 28, 7, 21, 32, 5, 43, 33, 15, 17, 34, 27, 41, 22, 10, 14, 23, 29, 42, 16, 11, 20, 2, 3, 40, 19, 12, 26, 4, 38, 44, 24, 13, 8, 31, 36, 1, 0, 30, 35, and 37.

FIG. 340 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 2/15.

According to the original GW pattern (A) of FIG. 340, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 3, 38, 9, 34, 6, 4, 18, 15, 1, 21, 19, 42, 20, 12, 13, 30, 26, 14, 2, 10, 35, 28, 44, 23, 11, 22, 16, 29, 40, 27, 37, 25, 41, 5, 43, 39, 36, 7, 24, 32, 17, 33, 8, and 0.

According to the converted GW pattern (B) of FIG. 340, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 31, 6, 21, 13, 10, 11, 27, 43, 3, 4, 19, 30, 35, 22, 37, 39, 38, 18, 42, 26, 28, 16, 25, 36, 9, 15, 20, 14, 44, 29, 41, 7, 34, 1, 12, 2, 23, 40, 5, 24, 32, 17, 33, 8, and 0.

FIG. 341 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 3/15.

According to the original GW pattern (A) of FIG. 341, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 22, 23, 26, 29, 27, 16, 1, 4, 25, 41, 21, 12, 2, 6, 8, 7, 19, 44, 42, 39, 40, 43, 35, 10, 28, 13, 15, 37, 32, 3, 24, 36, 38, 11, 18, 33, 30, 14, 9, 34, 20, 0, 17, and 31.

According to the converted GW pattern (B) of FIG. 341, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 27, 41, 8, 39, 28, 3, 18, 22, 16, 21, 7, 40, 13, 24, 33, 23, 1, 12, 19, 43, 15, 36, 30, 26, 4, 2, 44, 35, 37, 38, 14, 29, 25, 6, 42, 10, 32, 11, 9, 34, 20, 0, 17, and 31.

FIG. 342 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 4/15.

According to the original GW pattern (A) of FIG. 342, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 38, 20, 0, 34, 33, 41, 14, 30, 44, 7, 37, 8, 4, 9, 43, 15, 19, 32, 23, 5, 22, 26, 10, 12, 3, 31, 36, 21, 24, 11, 16, 18, 17, 29, 35, 42, 13, 40, 1, 28, 2, 25, 6, 39, and 27.

According to the converted GW pattern (B) of FIG. 342, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 38, 41, 37, 15, 22, 31, 16, 42, 20, 14, 8, 19, 26, 36, 18, 13, 0, 30, 4, 32, 10, 21, 17, 40, 34, 44, 9, 23, 12, 24, 29, 1, 33, 7, 43, 5, 3, 11, 35, 28, 2, 25, 6, 39, and 27.

FIG. 343 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 5/15.

According to the original GW pattern (A) of FIG. 343, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 4, 23, 3, 6, 18, 5, 0, 2, 7, 26, 21, 27, 39, 42, 38, 31, 1, 34, 20, 37, 40, 24, 43, 25, 33, 9, 22, 36, 30, 35, 11, 10, 17, 32, 13, 12, 41, 15, 14, 19, 16, 8, 44, 29, and 28.

According to the converted GW pattern (B) of FIG. 343, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 4, 5, 21, 31, 40, 9, 11, 12, 23, 0, 27, 1, 24, 22, 10, 41, 3, 2, 39, 34, 43, 36, 17, 15, 6, 7, 42, 20, 25, 30, 32, 14, 18, 26, 38, 37, 33, 35, 13, 19, 16, 8, 44, 29, and 28.

FIG. 344 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 6/15.

According to the original GW pattern (B) of FIG. 344, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 13, 25, 24, 14, 21, 1, 37, 2, 3, 11, 22, 18, 5, 10, 23, 12, 4, 26, 16, 38, 36, 33, 39, 0, 6, 7, 31, 32, 34, 27, 35, 15, 9, 30, 28, 19, 8, 20, 29, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 344, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 17, 2, 12, 0, 15, 13, 3, 4, 6, 9, 25, 11, 26, 7, 30, 24, 22, 16, 31, 28, 14, 18, 38, 32, 19, 21, 5, 36, 34, 8, 1, 10, 33, 27, 20, 37, 23, 39, 35, 29, 40, 41, 42, 43, and 44.

FIG. 345 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 7/15.

According to the original GW pattern (A) of FIG. 345, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 13, 16, 4, 12, 44, 15, 8, 14, 0, 3, 30, 20, 35, 21, 10, 6, 19, 17, 26, 39, 7, 24, 9, 27, 5, 37, 23, 32, 40, 31, 38, 42, 34, 25, 36, 2, 22, 43, 33, 28, 1, 18, 11, 41, and 29.

According to the converted GW pattern (B) of FIG. 345, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 13, 15, 30, 6, 7, 37, 38, 2, 16, 8, 20, 19, 24, 23, 42, 22, 4, 14, 35, 17, 9, 32, 34, 43, 12, 0, 21, 26, 27, 40, 25, 33, 44, 3, 10, 39, 5, 31, 36, 28, 1, 18, 11, 41, and 29.

FIG. 346 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 8/15.

According to the original GW pattern (A) of FIG. 346, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 41, 2, 12, 6, 33, 1, 13, 11, 26, 10, 39, 43, 36, 23, 42, 7, 44, 20, 8, 38, 18, 22, 24, 40, 4, 28, 29, 19, 14, 5, 9, 0, 30, 25, 35, 37, 27, 32, 31, 34, 21, 3, 15, 17, and 16.

According to the converted GW pattern (B) of FIG. 346, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 41, 1, 39, 7, 18, 28, 9, 37, 2, 13, 43, 44, 22, 29, 0, 27, 12, 11, 36, 20, 24, 19, 30, 32, 6, 26, 23, 8, 40, 14, 25, 31, 33, 10, 42, 38, 4, 5, 35, 34, 21, 3, 15, 17, and 16.

FIG. 347 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 9/15.

According to the original GW pattern (A) of FIG. 347, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 7, 9, 22, 10, 12, 3, 43, 6, 4, 24, 13, 14, 11, 15, 18, 19, 17, 16, 41, 25, 26, 20, 23, 21, 33, 31, 28, 39, 36, 30, 37, 27, 32, 34, 35, 29, 2, 42, 0, 1, 8, 40, 38, and 44.

According to the converted GW pattern (B) of FIG. 347, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 5, 12, 24, 18, 25, 33, 30, 35, 7, 3, 13, 19, 26, 31, 37, 29, 9, 43, 14, 17, 20, 28, 27, 2, 22, 6, 11, 16, 23, 39, 32, 42, 10, 4, 15, 41, 21, 36, 34, 0, 1, 8, 40, 38, and 44.

FIG. 348 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 10/15.

According to the original GW pattern (A) of FIG. 348, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 28, 20, 18, 38, 39, 2, 3, 30, 19, 4, 14, 36, 7, 0, 25, 17, 10, 6, 33, 15, 8, 26, 42, 24, 11, 21, 23, 5, 40, 41, 29, 32, 37, 44, 43, 31, 35, 34, 22, 1, 16, 27, 9, 13, and 12.

According to the converted GW pattern (B) of FIG. 348, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 28, 2, 14, 17, 8, 21, 29, 31, 20, 3, 36, 10, 26, 23, 32, 35, 18, 30, 7, 6, 42, 5, 37, 34, 38, 19, 0, 33, 24, 40, 44, 22, 39, 4, 25, 15, 11, 41, 43, 1, 16, 27, 9, 13, and 12.

FIG. 349 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 11/15.

According to the original GW pattern (B) of FIG. 349, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 8, 13, 0, 11, 9, 4, 36, 37, 16, 3, 10, 14, 24, 20, 33, 34, 25, 2, 21, 31, 12, 19, 7, 5, 27, 23, 26, 1, 18, 22, 35, 6, 32, 30, 28, 15, 29, 17, 39, 38, 40, 41, 42, 43, and 44.

According to the converted GW pattern (A) of FIG. 349, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 8, 16, 25, 27, 32, 13, 3, 2, 23, 30, 0, 10, 21, 26, 28, 11, 14, 31, 1, 15, 9, 24, 12, 18, 29, 4, 20, 19, 22, 17, 36, 33, 7, 35, 39, 37, 34, 5, 6, 38, 40, 41, 42, 43, and 44.

FIG. 350 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 12/15.

According to the original GW pattern (A) of FIG. 350, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 28, 21, 10, 15, 8, 22, 26, 2, 14, 1, 27, 3, 39, 20, 34, 25, 12, 6, 7, 40, 30, 29, 38, 16, 43, 33, 4, 35, 9, 32, 5, 36, 0, 41, 37, 18, 17, 13, 24, 42, 31, 23, 19, 11, and 44.

According to the converted GW pattern (B) of FIG. 350, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 28, 22, 27, 25, 30, 33, 5, 18, 21, 26, 3, 12, 29, 4, 36, 17, 10, 2, 39, 6, 38, 35, 0, 13, 15, 14, 20, 7, 16, 9, 41, 24, 8, 1, 34, 40, 43, 32, 37, 42, 31, 23, 19, 11, and 44.

FIG. 351 is a diagram showing an example of the GW pattern for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM and the code rate r is 13/15.

According to the original GW pattern (A) of FIG. 351, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 9, 13, 10, 7, 11, 6, 1, 14, 12, 8, 21, 15, 4, 36, 25, 30, 24, 28, 29, 20, 27, 5, 18, 17, 22, 33, 0, 16, 23, 31, 42, 3, 40, 39, 41, 43, 37, 44, 26, 2, 19, 38, 32, 35, and 34.

According to the converted GW pattern (B) of FIG. 351, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 9, 6, 21, 30, 27, 33, 42, 43, 13, 1, 15, 24, 5, 0, 3, 37, 10, 14, 4, 28, 18, 16, 40, 44, 7, 12, 36, 29, 17, 23, 39, 26, 11, 8, 25, 20, 22, 31, 41, 2, 19, 38, 32, 35, and 34.

Relationship Between Original GW Pattern and Converted GW Pattern

Next, the relationship between the original GW pattern and the converted GW pattern for each code length N of 64 k bits or 16 k bits for each modulation scheme will be described.

Here, the relationship between the GW pattern (A) and the GW pattern (B) when the GW pattern for the block interleaving of the type A (hereinafter, described as a GW pattern (A)) is set as the original GW pattern (A) and the GW pattern for the block interleaving of the type B (hereinafter, described as a GW pattern (B)) is set as the converted GW pattern (B) will be described.

For the sake of convenience in the description, only a case where the GW pattern (A) is set as the original GW pattern (A) and the GW pattern (B) is set as the converted GW pattern (B) will be described below, but it is possible to obtained the same relationship in a case where the GW pattern (B) is set as the original GW pattern (B) and the GW pattern (A) is set as the converted GW pattern (A).

FIG. 352 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is QPSK.

In FIG. 352, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 352, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 90, 1, 91, 2, 92, 3, 93, 4, 94, 5, 95, 6, 96, 7, 97, 8, 98, 9, 99, 10, 100, 11, 101, 12, 102, 13, 103, 14, 104, 15, 105, 16, 106, 17, 107, 18, 108, 19, 109, 20, 110, 21, 111, 22, 112, 23, 113, 24, 114, 25, 115, 26, 116, 27, 117, 28, 118, 29, 119, 30, 120, 31, 121, 32, 122, 33, 123, 34, 124, 35, 125, 36, 126, 37, 127, 38, 128, 39, 129, 40, 130, 41, 131, 42, 132, 43, 133, 44, 134, 45, 135, 46, 136, 47, 137, 48, 138, 49, 139, 50, 140, 51, 141, 52, 142, 53, 143, 54, 144, 55, 145, 56, 146, 57, 147, 58, 148, 59, 149, 60, 150, 61, 151, 62, 152, 63, 153, 64, 154, 65, 155, 66, 156, 67, 157, 68, 158, 69, 159, 70, 160, 71, 161, 72, 162, 73, 163, 74, 164, 75, 165, 76, 166, 77, 167, 78, 168, 79, 169, 80, 170, 81, 171, 82, 172, 83, 173, 84, 174, 85, 175, 86, 176, 87, 177, 88, 178, 89, and 179.

FIG. 353 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is 16-QAM.

In FIG. 353, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 353, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 45, 90, 135, 1, 46, 91, 136, 2, 47, 92, 137, 3, 48, 93, 138, 4, 49, 94, 139, 5, 50, 95, 140, 6, 51, 96, 141, 7, 52, 97, 142, 8, 53, 98, 143, 9, 54, 99, 144, 10, 55, 100, 145, 11, 56, 101, 146, 12, 57, 102, 147, 13, 58, 103, 148, 14, 59, 104, 149, 15, 60, 105, 150, 16, 61, 106, 151, 17, 62, 107, 152, 18, 63, 108, 153, 19, 64, 109, 154, 20, 65, 110, 155, 21, 66, 111, 156, 22, 67, 112, 157, 23, 68, 113, 158, 24, 69, 114, 159, 25, 70, 115, 160, 26, 71, 116, 161, 27, 72, 117, 162, 28, 73, 118, 163, 29, 74, 119, 164, 30, 75, 120, 165, 31, 76, 121, 166, 32, 77, 122, 167, 33, 78, 123, 168, 34, 79, 124, 169, 35, 80, 125, 170, 36, 81, 126, 171, 37, 82, 127, 172, 38, 83, 128, 173, 39, 84, 129, 174, 40, 85, 130, 175, 41, 86, 131, 176, 42, 87, 132, 177, 43, 88, 133, 178, 44, 89, 134, and 179.

FIG. 354 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is 64-QAM.

In FIG. 354, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 354, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 30, 60, 90, 120, 150, 1, 31, 61, 91, 121, 151, 2, 32, 62, 92, 122, 152, 3, 33, 63, 93, 123, 153, 4, 34, 64, 94, 124, 154, 5, 35, 65, 95, 125, 155, 6, 36, 66, 96, 126, 156, 7, 37, 67, 97, 127, 157, 8, 38, 68, 98, 128, 158, 9, 39, 69, 99, 129, 159, 10, 40, 70, 100, 130, 160, 11, 41, 71, 101, 131, 161, 12, 42, 72, 102, 132, 162, 13, 43, 73, 103, 133, 163, 14, 44, 74, 104, 134, 164, 15, 45, 75, 105, 135, 165, 16, 46, 76, 106, 136, 166, 17, 47, 77, 107, 137, 167, 18, 48, 78, 108, 138, 168, 19, 49, 79, 109, 139, 169, 20, 50, 80, 110, 140, 170, 21, 51, 81, 111, 141, 171, 22, 52, 82, 112, 142, 172, 23, 53, 83, 113, 143, 173, 24, 54, 84, 114, 144, 174, 25, 55, 85, 115, 145, 175, 26, 56, 86, 116, 146, 176, 27, 57, 87, 117, 147, 177, 28, 58, 88, 118, 148, 178, 29, 59, 89, 119, 149, and 179.

FIG. 355 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is 256-QAM.

In FIG. 355, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 355, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 22, 44, 66, 88, 110, 132, 154, 1, 23, 45, 67, 89, 111, 133, 155, 2, 24, 46, 68, 90, 112, 134, 156, 3, 25, 47, 69, 91, 113, 135, 157, 4, 26, 48, 70, 92, 114, 136, 158, 5, 27, 49, 71, 93, 115, 137, 159, 6, 28, 50, 72, 94, 116, 138, 160, 7, 29, 51, 73, 95, 117, 139, 161, 8, 30, 52, 74, 96, 118, 140, 162, 9, 31, 53, 75, 97, 119, 141, 163, 10, 32, 54, 76, 98, 120, 142, 164, 11, 33, 55, 77, 99, 121, 143, 165, 12, 34, 56, 78, 100, 122, 144, 166, 13, 35, 57, 79, 101, 123, 145, 167, 14, 36, 58, 80, 102, 124, 146, 168, 15, 37, 59, 81, 103, 125, 147, 169, 16, 38, 60, 82, 104, 126, 148, 170, 17, 39, 61, 83, 105, 127, 149, 171, 18, 40, 62, 84, 106, 128, 150, 172, 19, 41, 63, 85, 107, 129, 151, 173, 20, 42, 64, 86, 108, 130, 152, 174, 21, 43, 65, 87, 109, 131, 153, 175, 176, 177, 178, and 179.

FIG. 356 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is 1024-QAM.

In FIG. 356, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 356, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 18, 36, 54, 72, 90, 108, 126, 144, 162, 1, 19, 37, 55, 73, 91, 109, 127, 145, 163, 2, 20, 38, 56, 74, 92, 110, 128, 146, 164, 3, 21, 39, 57, 75, 93, 111, 129, 147, 165, 4, 22, 40, 58, 76, 94, 112, 130, 148, 166, 5, 23, 41, 59, 77, 95, 113, 131, 149, 167, 6, 24, 42, 60, 78, 96, 114, 132, 150, 168, 7, 25, 43, 61, 79, 97, 115, 133, 151, 169, 8, 26, 44, 62, 80, 98, 116, 134, 152, 170, 9, 27, 45, 63, 81, 99, 117, 135, 153, 171, 10, 28, 46, 64, 82, 100, 118, 136, 154, 172, 11, 29, 47, 65, 83, 101, 119, 137, 155, 173, 12, 30, 48, 66, 84, 102, 120, 138, 156, 174, 13, 31, 49, 67, 85, 103, 121, 139, 157, 175, 14, 32, 50, 68, 86, 104, 122, 140, 158, 176, 15, 33, 51, 69, 87, 105, 123, 141, 159, 177, 16, 34, 52, 70, 88, 106, 124, 142, 160, 178, 17, 35, 53, 71, 89, 107, 125, 143, 161, and 179.

FIG. 357 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 64 k bits when the modulation scheme is 4096-QAM.

In FIG. 357, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 177, 178, 179 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 357, the arrangement of bit groups 0 to 179 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 1, 16, 31, 46, 61, 76, 91, 106, 121, 136, 151, 166, 2, 17, 32, 47, 62, 77, 92, 107, 122, 137, 152, 167, 3, 18, 33, 48, 63, 78, 93, 108, 123, 138, 153, 168, 4, 19, 34, 49, 64, 79, 94, 109, 124, 139, 154, 169, 5, 20, 35, 50, 65, 80, 95, 110, 125, 140, 155, 170, 6, 21, 36, 51, 66, 81, 96, 111, 126, 141, 156, 171, 7, 22, 37, 52, 67, 82, 97, 112, 127, 142, 157, 172, 8, 23, 38, 53, 68, 83, 98, 113, 128, 143, 158, 173, 9, 24, 39, 54, 69, 84, 99, 114, 129, 144, 159, 174, 10, 25, 40, 55, 70, 85, 100, 115, 130, 145, 160, 175, 11, 26, 41, 56, 71, 86, 101, 116, 131, 146, 161, 176, 12, 27, 42, 57, 72, 87, 102, 117, 132, 147, 162, 177, 13, 28, 43, 58, 73, 88, 103, 118, 133, 148, 163, 178, 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, and 179.

FIG. 358 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 16 k bits when the modulation scheme is QPSK.

In FIG. 358, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 42, 43, 44 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 358, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 22, 1, 23, 2, 24, 3, 25, 4, 26, 5, 27, 6, 28, 7, 29, 8, 30, 9, 31, 10, 32, 11, 33, 12, 34, 13, 35, 14, 36, 15, 37, 16, 38, 17, 39, 18, 40, 19, 41, 20, 42, 21, 43, and 44.

FIG. 359 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 16 k bits when the modulation scheme is 16-QAM.

In FIG. 359, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 42, 43, 44 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 359, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 11, 22, 33, 1, 12, 23, 34, 2, 13, 24, 35, 3, 14, 25, 36, 4, 15, 26, 37, 5, 16, 27, 38, 6, 17, 28, 39, 7, 18, 29, 40, 8, 19, 30, 41, 9, 20, 31, 42, 10, 21, 32, 43, and 44.

FIG. 360 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 16 k bits when the modulation scheme is 64-QAM.

In FIG. 360, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 42, 43, 44 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 360, the arrangement of bit groups 0 to 44 of the LDPC code of 16 k bits is interleaved into the arrangement of bit groups 0, 7, 14, 21, 28, 35, 1, 8, 15, 22, 29, 36, 2, 9, 16, 23, 30, 37, 3, 10, 17, 24, 31, 38, 4, 11, 18, 25, 32, 39, 5, 12, 19, 26, 33, 40, 6, 13, 20, 27, 34, 41, 42, 43, and 44.

FIG. 361 is a diagram showing the relationship between the GW pattern (A) and the GW pattern (B) for the LDPC code having the code length N of 16 k bits when the modulation scheme is 256-QAM.

In FIG. 361, the GW pattern (A) of the GW pattern of 0, 1, 2, . . . , 42, 43, 44 may be rewritten into the GW pattern (B).

According to the GW pattern (B) of FIG. 361, the arrangement of bit groups 0 to 44 of the LDPC code of 64 k bits is interleaved into the arrangement of bit groups 0, 5, 10, 15, 20, 25, 30, 35, 1, 6, 11, 16, 21, 26, 31, 36, 2, 7, 12, 17, 22, 27, 32, 37, 3, 8, 13, 18, 23, 28, 33, 38, 4, 9, 14, 19, 24, 29, 34, 39, 40, 41, 42, 43, and 44.

Configuration Example of Bit Deinterleaver 165

FIG. 362 is a block diagram showing a configuration example of the bit deinterleaver 165 of FIG. 207.

The bit deinterleaver 165 includes a block deinterleaver 1031 and a group-wise deinterleaver 1032, and performs (bit) deinterleaving on the symbol bits of the symbol which is the data from the demapper 164 (FIG. 207).

That is, the block deinterleaver 1031 performs the block deinterleaving (reverse processing of the block interleaving) corresponding to the block interleaving performed by the block interleaver 1022 of FIG. 217 on the symbol bits of the symbol from the demapper 164 as a target, that is, the block deinterleaving that returns the positions of (the likelihood of) the code bits of the LDPC code rearranged through the block interleaving to the original positions, and supplies an LDPC code obtained as the result to the group-wise deinterleaver 1032.

The block deinterleaver 1031 corresponds to the block deinterleaving of the type A or the type B, and can perform the block deinterleaving of the type A or the type B.

The group-wise deinterleaver 1032 performs the group-wise deinterleaving (reverse processing of the group-wise interleaving) corresponding to the group-wise interleaving performed by the group-wise interleaver 1021 of FIG. 217 on the LDPC code from the block deinterleaver 1031 as a target, that is, the group-wise deinterleaving that returns the arrangement of the code bits to the original arrangement by, for example, rearranging the code bits of the LDPC code in which the arrangement has been changed for every bit group through the group-wise interleaving for every bit group.

Here, when it is assumed that the block deinterleaving of the type A is performed, the group-wise deinterleaver 1032 rewrites the GW pattern for the block interleaving of the type A into the GW pattern for the block deinterleaving of the type B when the block deinterleaving of the type B is performed. That is, in this case, in the group-wise deinterleaver 1032, the original GW pattern (A) is rewritten into the converted GW pattern (B).

When it is assumed that the block deinterleaving of the type B is performed, the group-wise deinterleaver 1032 rewrites the GW pattern for the block deinterleaving of the type B into the GW pattern for the block deinterleaving of the type A when the block deinterleaving of the type A is performed. That is, in this case, in the group-wise deinterleaver 1032, the original GW pattern (B) is rewritten into the converted GW pattern (A).

When the parity interleaving, the group-wise interleaving and the block interleaving are performed on the LDPC code supplied to the bit deinterleaver 165 from the demapper 164, the bit deinterleaver 165 can perform all of the parity deinterleaving (reverse processing of the parity interleaving, that is, the parity deinterleaving that returns the code bits of the LDPC code in which the arrangement has been changed through the parity interleaving to the original arrangement) corresponding to the parity interleaving, the block deinterleaving corresponding to the block interleaving, and the group-wise deinterleaving corresponding to the group-wise interleaving.

However, in the bit deinterleaver 165 of FIG. 362, the block deinterleaver 1031 that performs the block deinterleaving corresponding to the block interleaving, and the group-wise deinterleaver 1032 that performs the group-wise deinterleaving corresponding to the group-wise interleaving are provided, but the block that performs the parity deinterleaving corresponding to the parity interleaving is not provided, and the parity deinterleaving is not performed.

Accordingly, the LDPC code on which the block deinterleaving and the group-wise deinterleaving have been performed and the parity deinterleaving has not been performed is supplied to the LDPC decoder 166 from (the group-wise deinterleaver 1032 of) the bit deinterleaver 165.

The LDPC decoder 166 performs the LDPC decoding on the LDPC code from the bit deinterleaver 165 by using the transformation check matrix obtained by performing at least the column permutation corresponding to the parity interleaving on the parity check matrix H of the DVB method using the LDPC encoding by the LDPC encoder 115 of FIG. 8 (or the transformation check matrix (FIG. 29) obtained by performing the row permutation on the parity check matrix of the ETRI method (FIG. 27)), and outputs the data obtained as the result as the decoded result of the LDPC target data.

Configuration Example of Block Deinterleaver 1031 Corresponding to Block Deinterleaving of Type A

FIG. 363 is a block diagram showing a configuration example of the block deinterleaver 1031 of FIG. 362.

The block deinterleaver 1031 corresponding to the block deinterleaving of the type A has the same configuration as that of the block interleaver 1022 corresponding to the block interleaving of the type A described in FIG. 218.

Accordingly, the block deinterleaver 1031 includes a storage region called a part 1, and a storage region called a part 2, and both of the parts 1 and 2 are configured in such a manner that columns as storage regions which store one bit in the row direction and store a predetermined number of bits in the column direction are arranged by the number C equal to the number of bits m of the symbol.

The block deinterleaver 1031 performs the block deinterleaving of the type A by writing and reading the LDPC code in and from the parts 1 and 2.

In the block deinterleaving of the type A, the writing of the LDPC code (as the symbol) is performed in reading order of the LDPC code performed by the block interleaver 1022 of FIG. 218.

Further, in the block deinterleaving of the type A, the reading of the LDPC code is performed in writing order of the LDPC code performed by the block interleaver 1022 of FIG. 218.

That is, in the block interleaving of the type A by the block interleaver 1022 of FIG. 218, although the LDPC code is written in the column direction and is read in the row direction with respect to the parts 1 and 2, in the block deinterleaving of the type A by the block deinterleaver 1031 of FIG. 363, the LDPC code is written in the row direction and is read in the column direction with respect to the parts 1 and 2.

Configuration Example of Block Deinterleaver 1031 Corresponding to Block Deinterleaving of Type B

FIG. 364 is a block diagram showing a configuration example of a block deinterleaver 1031 of FIG. 362.

The block deinterleaver 1031 corresponding to the block deinterleaving of the type B has the same configuration as that of the block interleaver 1022 corresponding to the block interleaving of the type B described in FIG. 224.

Accordingly, the block deinterleaver 1031 includes a storage region called a part 1, and a storage region called a part 2.

The part 1 is configured in such a manner that columns as storage regions which store one bit in the row direction and store a predetermined number of bits in the column direction are arranged in the row direction by the number C equal to the number of bits m of the symbol. The part 2 is configured in such a manner that rows as storage regions which store one bit in the column direction and store a predetermined number of bits in the row direction.

The block deinterleaver 1031 performs the block deinterleaving of the type B by writing and reading the LDPC code in and from the parts 1 and 2.

However, in the block deinterleaving of the type B, the writing of the LDPC code (as the symbol) is performed in reading order of the LDPC code performed by the block interleaver 1022 of FIG. 224.

Moreover, in the block deinterleaving of the type B, the reading of the LDPC code is performed in writing order of the LDPC code performed by the block interleaver 1022 of FIG. 224.

That is, in the block interleaving of the type B by the block interleaver 1022 of FIG. 224, since the LDPC code is written in the row direction and read in the row direction with respect to the parts 1 and 2, in the block deinterleaving of the type B by the block deinterleaver 1031 of FIG. 364, the LDPC code is written in the row direction and is read in the row direction with respect to the parts 1 and 2.

Another Configuration Example of Bit Deinterleaver 165

FIG. 365 is a block diagram showing another configuration example of the bit deinterleaver 165 of FIG. 207.

In the drawing, the parts corresponding to those in FIG. 362 will be assigned the same reference numerals, and the description thereof will be appropriately omitted in the following description.

That is, the bit deinterleaver 165 of FIG. 365 has the same configuration as that in FIG. 362 except for the fact that a parity deinterleaver 1011 is newly provided.

In FIG. 365, the bit deinterleaver 165 includes the block deinterleaver 1031, the group-wise deinterleaver 1032, and the parity deinterleaver 1011, and performs the bit deinterleaving on the code bits of the LDPC code from the demapper 164.

That is, the block deinterleaver 1031 performs the block deinterleaving (reverse processing of the block interleaving) corresponding to the block interleaving performed by the block interleaver 1022 of the transmission apparatus 11 on the LDP code from the demapper 164 as a target, that is, the block deinterleaving that returns the positions of the code bits replaced through the block interleaving to the original positions, and supplies an LDPC code obtained as the result to the group-wise deinterleaver 1032.

The group-wise deinterleaver 1032 performs the group-wise deinterleaving corresponding to the group-wise interleaving as the rearranging process performed by the group-wise interleaver 1021 of the transmission apparatus 11 on the LDPC code from the block deinterleaver 1031 as a target.

The LDPC code obtained as the result of the group-wise deinterleaving is supplied to the parity deinterleaver 1011 from the group-wise deinterleaver 1032.

The parity deinterleaving performed by the parity deinterleaver 1011 and the LDPC decoding on the LDPC code performed by the LDPC decoder 166 are the same as those in FIG. 216, and thus, the description thereof will be omitted below.

For the sake of convenience in the description, although it has been described in FIG. 365 that the block deinterleaver 1031 that performs the block deinterleaving, the group-wise deinterleaver 1032 that performs the group-wise deinterleaving and the parity deinterleaver 1011 that performs the parity deinterleaving are individually provided, two or more of the block deinterleaver 1031, the group-wise deinterleaver 1032 and the parity deinterleaver 1011 may be integrally configured similarly to the parity interleaver 23, the group-wise interleaver 1021 and the block interleaver 1022 of the transmission apparatus 11.

Configuration Example of Reception System

FIG. 366 is a block diagram showing a first configuration example of a reception system to which the reception apparatus 12 can be applied.

In FIG. 366, the reception system includes an acquisition unit 1101, a transmission channel decoding unit 1102, and an information source decoding unit 1103.

The acquisition unit 1101 obtains a signal including the LDPC code obtained by performing at least the LDPC encoding on the LDPC target data such as image data or voice data of a program through a non-illustrated transmission channel (communication channel) such as terrestrial digital broadcasting, satellite digital broadcasting, a CATV network, or other networks other than the Internet, and supplies the obtained signal to the transmission channel decoding unit 1102.

Here, when the signal obtained by the acquisition unit 1101 is broadcasted from, for example, a broadcasting station through the terrestrial digital broadcasting, the satellite digital broadcasting, or the cable television (CATV) network, the acquisition unit 1101 is configured as a tuner or a set-top box (STB). When the signal obtained by the acquisition unit 1101 is transmitted using, for example, multicast such as an internet protocol television (IPTV) from a web server, the acquisition unit 1101 is configured as a network interface (I/F) such as a network interface card (NIC).

The transmission channel decoding unit 1102 corresponds to the reception apparatus 12. The transmission channel decoding unit 1102 performs transmission channel decoding including at least a process of correcting an error occurring in a transmission channel on the signal obtained by the acquisition unit 1101 through the transmission channel, and supplies a signal obtained as the result to the information source decoding unit 1103.

That is, the signal obtained by the acquisition unit 1101 through the transmission channel is a signal obtained by performing at least an error correcting encoding for correcting the error in the transmission channel, and the transmission channel decoding unit 1102 performs the transmission channel decoding such as an error correcting process on the signal.

Here, examples of the error correcting encoding includes LDPC encoding and BCH encoding. Here, as the error correcting encoding, at least the LDPC encoding is performed.

In addition, the transmission channel decoding may include decoding on a modulation signal.

The information source decoding unit 1103 performs information source decoding including at least a process of decompressing compressed information to original information on the signal on which the transmission channel decoding has been performed.

That is, in order to reduce the amount of data such as image or voice as information, compression encoding that compresses the information may be performed on the signal obtained by the acquisition unit 1101 through the transmission channel, and in this case, the information source decoding unit 1103 performs the information source decoding such as the process (decompression process) of decompressing the compressed information to the original information on the signal on which the transmission channel decoding has been performed.

When the compression encoding has not been performed on the signal obtained by the acquisition unit 1101 through the transmission channel, the information source decoding unit 1103 does not perform the process of decompressing the compressed information to the original information.

Here, as the decompression process, there is, for example, a MPEG decoding. The transmission channel decoding may include descrambling in addition to the decompression process.

In the reception system having the aforementioned configuration, the compression encoding such as MPEG encoding is performed on data such as image or voice in the acquisition unit 1101, and the signal on which the error correcting encoding such as LDPC encoding has been performed is obtained through the transmission channel and is supplied to the transmission channel decoding unit 1102.

In the transmission channel decoding unit 1102, for example, the same process as that performed by the reception apparatus 12 is performed on the signal from the acquisition unit 1101, as the transmission channel decoding, and a signal obtained as the result is supplied to the information source decoding unit 1103.

In the information source decoding unit 1103, the information source decoding such as MPEG decoding is performed on the signal from the transmission channel decoding unit 1102, and an image or a voice obtained as the result is output.

For example, the reception system of FIG. 366 described above may be applied to a television tuner that receives television broadcasting as digital broadcasting.

The acquisition unit 1101, the transmission channel decoding unit 1102 and the information source decoding unit 1103 may be independently configured as one device (hardware (integrated circuit (IC)) or software).

With regard to the acquisition unit 1101, the transmission channel decoding unit 1102 and the information source decoding unit 1103, a set of the acquisition unit 1101 and the transmission channel decoding unit 1102, a set of the transmission channel decoding unit 1102 and the information source decoding unit 1103, and a set of the acquisition unit 1101, the transmission channel decoding unit 1102 and the information source decoding unit 1103 may be independently configured as one device.

FIG. 367 is a block diagram showing a second configuration example of the reception system to which the reception apparatus 12 can be applied.

In the drawing, the parts corresponding to those in FIG. 366 will be assigned the same reference numerals, and thus, the description thereof will be appropriately omitted.

The reception system of FIG. 367 has in common with the reception system of FIG. 366 in that the acquisition unit 1101, the transmission channel decoding unit 1102 and the information source decoding unit 1103 are provided, and has a difference from the reception system of FIG. 366 in that an output unit 1111 is newly provided.

The output unit 1111 is, for example, a display unit that displays an image or a speaker that outputs a voice, and outputs an image or a voice as the signal output from the information source decoding unit 1103. That is, the output unit 1111 displays the image or outputs the voice.

For example, the reception system of FIG. 367 described above may be applied to a TV (television receiver) that receives television broadcasting as digital broadcasting or a radio receiver that receives radio broadcasting.

When the compression encoding has not been performed on the signal obtained in the acquisition unit 1101, the signal output from the transmission channel decoding unit 1102 is supplied to the output unit 1111.

FIG. 368 is a block diagram showing a third configuration example of the reception system to which the reception apparatus 12 can be applied.

In the drawing, the parts corresponding to those in FIG. 366 will be assigned the same reference numerals, and thus, the description thereof will be appropriately omitted.

The reception system of FIG. 368 has in common with the reception system in FIG. 366 in that the acquisition unit 1101 and the transmission channel decoding unit 1102 are provided.

However, the reception system of FIG. 368 has a difference from the reception system of FIG. 366 in that the information source decoding unit 1103 is not provided and a recording unit 1121 is newly provided.

The recording unit 1121 records (stores) the signal (for example, TS packet of TS of MPEC) output from the transmission channel decoding unit 1102 in a recording (storing) medium such as an optical disc, a hard disc (magnetic disc), or a flash memory.

The reception system of FIG. 368 described above may be applied to a recorder that records television broadcasting.

In FIG. 368, the reception system includes the information source decoding unit 1103, and in the information source decoding unit 1103, the signal on which the information source decoding has been performed, that is, the image or the voice obtained through decoding can be recorded in the recording unit 1121.

Embodiment of Computer

Next, a series of processes described above may be performed by hardware or may be performed by software. When the series of processes is performed by software, programs constituting the software are installed in a general-purpose computer.

Here, FIG. 369 shows a configuration example of an embodiment of a computer in which the programs for executing the series of processes are installed.

The programs may be previously recorded in a hard disc 705 or a ROM 703 as a recording medium embedded in the computer.

Alternatively, the programs may be temporarily or permanently stored (recorded) in a removable recording medium 711 such as a flexible disc, a compact disc read-only memory (CD-ROM), a magneto-optical (MO) disc, a digital versatile disc (DVD), a magnetic disc, or a semiconductor memory. The removable recording medium 711 may be provided as so-called package software.

The programs may be installed in the computer from the removable recording medium 711, may be wirelessly transmitted to the computer from a download site through an artificial satellite for digital satellite broadcasting, or may be transmitted to the computer through a network such as a local area network (LAN) or the Internet in a wired manner. In the computer, the programs transmitted in this manner may be received by a communication unit 708, and may be installed in the hard disc 705 embedded therein.

The computer includes a central processing unit (CPU) 702. An input and output interface 710 is connected to the CPU 702 through a bus 701, and when an instruction is input by an operation input of an input unit 707 including a keyboard, a mouse or a microphone by a user through the input and output interface 710, the CPU 702 executes the programs stored in the read-only memory (ROM) 703 in response to the instruction. Alternatively, the CPU 702 downloads the programs stored in the hard disc 705, the programs which is transmitted from the satellite or the network, received by the communication unit 708 and installed in the hard disc 705, and the programs which is read from the removable recording medium 711 provided in a drive 709 and is installed in the hard disc 705 in a random-access memory (RAM) 704, and executes the downloaded programs. Thus, the CPU 702 performs the process according to the flowchart described above or the process performed by the configuration of the block diagram described above. The CPU 702 outputs the processed result from an output unit 706 including a liquid crystal display (LCD) or a speaker through, for example, the input and output interface 710 when necessary, transmits the processed result from the communication unit 708, or records the processed result in the hard disc 705.

Here, in the present specification, processing steps that describe the programs for causing the computer to perform various processes are not necessarily performed in a sequence of time in the order described as the flowchart, and may include processes which are executed in parallel or individual manner (for example, a parallel process or a process by objects).

Furthermore, the programs may be processed by one computer, or may be processed in a distributed manner by a plurality of computers. Further, the programs may be executed by being transmitted to a remote computer.

The embodiments of the present technology are not limited to the embodiments described above, and can be variously changed within the scope without departing from the gist of the present technology.

That is, for example, in (the parity check matrix initial value table of) the new LDPC encoding described above, the communication channel 13 (FIG. 7) may use a satellite channel, a terrestrial channel, or a cable (wired channel), and other channels. The new LDPC code may be used in data transmission other then digital broadcasting.

The GW pattern described above may be applied to encoding other than the new LDPC encoding. Moreover, a modulation scheme to which the GW pattern described above is applied is not limited to QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM or 4096-QAM.

The effects described in the present specification are merely examples, and are not limited. Other effects may be obtained. 

What is claimed is:
 1. A data processing apparatus comprising: a group-wise interleaving unit that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits; and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme, wherein a type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed, wherein a MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed, and wherein when the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.
 2. A data processing method comprising: group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits; and block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme, wherein a type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed, wherein a MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed, and wherein when the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, in the group-wise interleaving, the group-wise interleaving is performed on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, in the group-wise interleaving, the group-wise interleaving is performed on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.
 3. A data processing apparatus comprising: a block deinterleaving unit that performs block deinterleaving which returns m bits of a symbol obtained from data transmitted from a transmission apparatus to an LDPC code obtained by performing group-wise interleaving; and a group-wise deinterleaving unit that performs group-wise deinterleaving which returns the arrangement of the LDPC code obtained by performing the group-wise interleaving on the original arrangement, wherein the transmission apparatus includes a group-wise interleaving unit that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits, and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme, wherein a type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed, wherein a MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed, and wherein when the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained.
 4. A data processing method comprising: block deinterleaving which returns m bits of a symbol obtained from data transmitted from a transmission apparatus to an LDPC code obtained by performing group-wise interleaving; and group-wise deinterleaving which returns the arrangement of the LDPC code obtained by performing the group-wise interleaving on the original arrangement, wherein the transmission apparatus includes a group-wise interleaving unit that performs group-wise interleaving which interleaves an LDPC code having a code length (N) of 16,200 bits or 64,800 bits for every bit group of 360 bits, and a block interleaving unit that performs block interleaving in such a manner that an LDPC code obtained by performing the group-wise interleaving is written in m number of columns as storage regions arranged in the row direction, m bits are obtained by respectively reading the LDPC code from m number of columns bit by bit, and the m bits are interleaved into one symbol corresponding to any one of 2^(m) number of signal points defined by a modulation scheme, wherein a type of the block interleaving includes a type A in which the writing of an LDPC code obtained by performing the group-wise interleaving in the column direction of the columns is iteratively performed on m number of columns, and a type B in which the writing of an LDPC code obtained by performing the group-wise interleaving in the row direction of m number of columns for every bit group is iteratively performed, wherein a MODCOD which is a combination of the LDPC code and the modulation scheme includes a MODCOD-A which is a MODCOD based on the assumption that the block interleaving of the type A is performed, and a MDOCOD-B which is a MDOCOD based on the assumption that the block interleaving of the type B is performed, and wherein when the block interleaving of the type A is performed on the LDPC code of the MODCOD-B, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MODCOD-B such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type B is performed is obtained, or when the block interleaving of the type B is performed on the LDPC code of the MODCOD-A, the group-wise interleaving unit performs the group-wise interleaving on the LDPC code of the MDOCOD-A such that the same block interleaving result as the block interleaving result obtained when the block interleaving of the type A is performed is obtained. 